Strict Feasibility of Variational Inequalities in Reflexive Banach Spaces
Yi Ran HE; Xiu Zhen MAO; Mi ZHOU
2007-01-01
Strict feasibility is proved to be an equivalent characterization of (dual) variational in-equalities having a nonempty bounded solution set, provided the mappings involved are stably properly quasimonotone. This generalizes an earlier result from finite-dimensional Euclidean spaces to infinite-dimensional reflexive Banach spaces. Moreover, the monotonicity-type assumptions are also mildly relaxed.
Every Weakly Compact Set Can Be Uniformly Embedded into a Reflexive Banach Space
Li Xin CHENG; Qing Jin CHENG; Zheng Hua LUO; Wen ZHANG
2009-01-01
Based on an application of the Davis-Figiel-Johnson-Pelzy(s)ki procedure,this note shows that every weakly compact subset of a Banach space can be uniformly embedded into a reflexive Banach space.As its application,we present the recent renorming theorems for reflexive spaces of Odellan arbitrary Banach space.
On extension results for n-cyclically monotone operators in reflexive Banach spaces
Bot, Radu Ioan
2009-01-01
In this paper we provide some extension results for n-cyclically monotone operators in reflexive Banach spaces by making use of the Fenchel duality. In this way we give a positive answer to a question posed by Bauschke and Wang in [4].
Hytönen, Tuomas; Veraar, Mark; Weis, Lutz
2016-01-01
The present volume develops the theory of integration in Banach spaces, martingales and UMD spaces, and culminates in a treatment of the Hilbert transform, Littlewood-Paley theory and the vector-valued Mihlin multiplier theorem. Over the past fifteen years, motivated by regularity problems in evolution equations, there has been tremendous progress in the analysis of Banach space-valued functions and processes. The contents of this extensive and powerful toolbox have been mostly scattered around in research papers and lecture notes. Collecting this diverse body of material into a unified and accessible presentation fills a gap in the existing literature. The principal audience that we have in mind consists of researchers who need and use Analysis in Banach Spaces as a tool for studying problems in partial differential equations, harmonic analysis, and stochastic analysis. Self-contained and offering complete proofs, this work is accessible to graduate students and researchers with a background in functional an...
Separably injective Banach spaces
Avilés, Antonio; Castillo, Jesús M F; González, Manuel; Moreno, Yolanda
2016-01-01
This monograph contains a detailed exposition of the up-to-date theory of separably injective spaces: new and old results are put into perspective with concrete examples (such as l∞/c0 and C(K) spaces, where K is a finite height compact space or an F-space, ultrapowers of L∞ spaces and spaces of universal disposition). It is no exaggeration to say that the theory of separably injective Banach spaces is strikingly different from that of injective spaces. For instance, separably injective Banach spaces are not necessarily isometric to, or complemented subspaces of, spaces of continuous functions on a compact space. Moreover, in contrast to the scarcity of examples and general results concerning injective spaces, we know of many different types of separably injective spaces and there is a rich theory around them. The monograph is completed with a preparatory chapter on injective spaces, a chapter on higher cardinal versions of separable injectivity and a lively discussion of open problems and further lines o...
On Hereditarily Indecomposable Banach Spaces
Li Xin CHENG; Huai Jie ZHONG
2006-01-01
This paper shows that every non-separable hereditarily indecomposable Banach space admits an equivalent strictly convex norm, but its bi-dual can never have such a one; consequently, every non-separable hereditarily indecomposable Banach space has no equivalent locally uniformly convex norm.
Albiac, Fernando
2016-01-01
This text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems. The two new chapters in this second edition are devoted to two topics of much current interest amongst functional analysts: Greedy approximation with respect to bases in Banach spaces and nonlinear geometry of Banach spaces. This new material is intended to present these two directions of research for their intrinsic importance within Banach space theory, and to motivate graduate students interested in learning more about them. This textbook assumes only a basic knowledge of functional analysis, giving the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special emphasis is placed on the study of the classical Lebesgue spaces Lp (and their sequence space analogues) and spaces of continuous f...
Banach spaces of universal disposition
Aviles, Antonio; Castillo, Jesus M F; Gonzalez, Manuel; Moreno, Yolanda
2011-01-01
In this paper we present a method to obtain Banach spaces of universal and almost-universal disposition with respect to a given class $\\mathfrak M$ of normed spaces. The method produces, among other, the Gurari\\u{\\i} space $\\mathcal G$ (the only separable Banach space of almost-universal disposition with respect to the class $\\mathfrak F$ of finite dimensional spaces), or the Kubis space $\\mathcal K$ (under {\\sf CH}, the only Banach space with the density character the continuum which is of universal disposition with respect to the class $\\mathfrak S$ of separable spaces). We moreover show that $\\mathcal K$ is not isomorphic to a subspace of any $C(K)$-space -- which provides a partial answer to the injective space problem-- and that --under {\\sf CH}-- it is isomorphic to an ultrapower of the Gurari\\u{\\i} space. We study further properties of spaces of universal disposition: separable injectivity, partially automorphic character and uniqueness properties.
Extremely strict ideals in Banach spaces
T S S R K RAO
2016-08-01
Motivated by the notion of an ideal introduced by Godefroy {\\it et al.} ({\\it Studia Math.} {\\bf 104} (1993) 13–59), in this article, we introduce and study the notion of an extremely strict ideal. For a Poulsen simplex $K$, we show that the space of affine continuous functions on $K$ is an extremely strict ideal in the space of continuous functions on $K$. For injective tensor product spaces, we prove a cancelation theorem for extremely strict ideals. We also exhibit non-reflexive Banach spaces which are not strict ideals in their fourth dual.
Fusion Frames and -Frames in Banach Spaces
Amir Khosravi; Behrooz Khosravi
2011-05-01
Fusion frames and -frames in Hilbert spaces are generalizations of frames, and frames were extended to Banach spaces. In this article we introduce fusion frames, -frames, Banach -frames in Banach spaces and we show that they share many useful properties with their corresponding notions in Hilbert spaces. We also show that -frames, fusion frames and Banach -frames are stable under small perturbations and invertible operators.
Smooth analysis in Banach spaces
Hájek, Petr
2014-01-01
This bookis aboutthe subject of higher smoothness in separable real Banach spaces.It brings together several angles of view on polynomials, both in finite and infinite setting.Also a rather thorough and systematic view of the more recent results, and the authors work is given. The book revolves around two main broad questions: What is the best smoothness of a given Banach space, and its structural consequences? How large is a supply of smooth functions in the sense of approximating continuous functions in the uniform topology, i.e. how does the Stone-Weierstrass theorem generalize into in
Computable Frames in Computable Banach Spaces
S.K. Kaushik
2016-06-01
Full Text Available We develop some parts of the frame theory in Banach spaces from the point of view of Computable Analysis. We define computable M-basis and use it to construct a computable Banach space of scalar valued sequences. Computable Xd frames and computable Banach frames are also defined and computable versions of sufficient conditions for their existence are obtained.
Characterizing R-duality in Banach spaces
Christensen, Ole; Xiao, Xiang Chun; Zhu, Yu Can
2013-01-01
R-duals of certain sequences in Hilbert spaces were introduced by Casazza, Kutyniok and Lammers in 2004 and later generalized to Banach spaces by Xiao and Zhu. In this paper we provide some characterizations of R-dual sequences in Banach spaces.......R-duals of certain sequences in Hilbert spaces were introduced by Casazza, Kutyniok and Lammers in 2004 and later generalized to Banach spaces by Xiao and Zhu. In this paper we provide some characterizations of R-dual sequences in Banach spaces....
Existence of zeros for operators taking their values in the dual of a Banach space
Ricceri Biagio
2004-01-01
Full Text Available Using continuous selections, we establish some existence results about the zeros of weakly continuous operators from a paracompact topological space into the dual of a reflexive real Banach space.
Best Simultaneous Approximation to Totally Bounded Sequences in Banach Spaces
Xian Fa LUO; Chong LI; Genaro LOPEZ
2008-01-01
This paper is concerned with the problem of best weighted simultaneous approximations to totally bounded sequences in Banach spaces. Characterization results from convex sets in Banach spaces are established under the assumption that the Banach space is uniformly smooth.
Regularization methods in Banach spaces
Schuster, Thomas; Hofmann, Bernd; Kazimierski, Kamil S
2012-01-01
Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Usually the mathematical model of an inverse problem consists of an operator equation of the first kind and often the associated forward operator acts between Hilbert spaces. However, for numerous problems the reasons for using a Hilbert space setting seem to be based rather on conventions than on an approprimate and realistic model choice, so often a Banach space setting would be closer to reality. Furthermore, sparsity constraints using general Lp-norms or the B
Quotients of Banach spaces and surjectively universal spaces
Dodos, Pandelis
2010-01-01
We characterize those classes $\\mathcal{C}$ of separable Banach spaces for which there exists a separable Banach space $Y$ not containing $\\ell_1$ and such that every space in the class $\\mathcal{C}$ is a quotient of $Y$.
The Connection Between the Metric and Generalized Projection Operators in Banach Spaces
Yakov ALBER; Jin Lu LI
2007-01-01
In this paper we study the connection between the metric projection operator PK:B→K,where B is a reflexive Banach space with dual space B* and K is a non-empty closed convex subset of B, and the generalized projection oprators Πk:B→k and πk:B*→k.We also present some results in non-reflexive Banach spaces.
Strongly Irreducible Operators on Banach Spaces
Yun Nan ZHANG; Huai Jie ZHONG
2012-01-01
This paper firstly discusses the existence of strongly irreducible operators on Banach spaces.It shows that there exist strongly irreducible operators on Banach spaces with w*-separable dual.It also gives some properties of strongly irreducible operators on Banach spaces. In particular,if T is a strongly irreducible operator on an infinite-dimensional Banach space,then T is not of finite rank and T is not an algebraic operator. On Banach spaces with subsymmetric bases,including infinite-dimensional separable Hilbert spaces,it shows that quasisimilarity does not preserve strong irreducibility.In addition,we show that the strong irreducibility of an operator does not imply the strong irreducibility of its conjugate operator,which is not the same as the property in Hilbert spaces.
On Peano's theorem in Banach spaces
Hájek, Petr
2009-01-01
We show that if $X$ is an infinite-dimensional separable Banach space (or more generally a Banach space with an infinite-dimensional separable quotient) then there is a continuous mapping $f\\colon X\\to X$ such that the autonomous differential equation $x'=f(x)$ has no solution at any point.
Banach spaces of analytic functions
Hoffman, Kenneth
2007-01-01
A classic of pure mathematics, this advanced graduate-level text explores the intersection of functional analysis and analytic function theory. Close in spirit to abstract harmonic analysis, it is confined to Banach spaces of analytic functions in the unit disc.The author devotes the first four chapters to proofs of classical theorems on boundary values and boundary integral representations of analytic functions in the unit disc, including generalizations to Dirichlet algebras. The fifth chapter contains the factorization theory of Hp functions, a discussion of some partial extensions of the f
On Uniform Convexity of Banach Spaces
Qing Jin CHENG; Bo WANG; Cui Ling WANG
2011-01-01
This paper gives some relations and properties of several kinds of generalized convexity in Banach spaces. As a result, it proves that every kind of uniform convexity implies the Banach-Sakes property, and several notions of uniform convexity in literature are actually equivalent.
q-Besselian Frames in Banach Spaces
Yu Can ZHU
2007-01-01
In this paper, we introduce the concepts of q-Besselian frame and (p, σ)-near Riesz basis in a Banach space, where σ is a finite subset of positive integers and 1/p + 1/q=1 with p 1, q 1, and determine the relations among q-frame, p-Riesz basis, q-Besselian frame and (p, σ)-near Riesz basis in a Banach space. We also give some sufficient and necessary conditions on a q-Besselian frame for a Banach space. In particular, we prove reconstruction formulas for Banach1 spaces X and X* that if {Xn}∞n=1(∪)X is a q-Besselian frame for X, then there exists a p-Besselian frame {y*n}∞n=1(∪) X* for X* such that x = ∑∞n-1 y*n(x)xn for all x ∈ X, and x = ∑∞n-1 x*xny*n, for all x* ∈ X*. Lastly, we consider the stability of a q-Besselian frame for the Banach space X under perturbation. Some results of J. R. Holub, P. G. Casazza, O. Christensen and others in Hilbert spaces are extended to Banach spaces.
Bloch spaces on bounded symmetric domains in complex Banach spaces
DENG; Fangwen
2006-01-01
We give a definition of Bloch space on bounded symmetric domains in arbitrary complex Banach space and prove such function space is a Banach space. The properties such as boundedness, compactness and closed range of composition operators on such Bloch space are studied.
On Λ-Type Duality of Frames in Banach Spaces
Renu Chugh
2013-11-01
Full Text Available Frames are redundant system which are useful in the reconstruction of certain classes of spaces. The dual of a frame (Hilbert always exists and can be obtained in a natural way. Due to the presence of three Banach spaces in the definition of retro Banach frames (or Banach frames duality of frames in Banach spaces is not similar to frames for Hilbert spaces. In this paper we introduce the notion of Λ-type duality of retro Banach frames. This can be generalized to Banach frames in Banach spaces. Necessary and sufficient conditions for the existence of the dual of retro Banach frames are obtained. A special class of retro Banach frames which always admit a dual frame is discussed.
Banach spaces of continuous functions as dual spaces
Dales, H G; Lau, A T -M; Strauss, D
2016-01-01
This book gives a coherent account of the theory of Banach spaces and Banach lattices, using the spaces C_0(K) of continuous functions on a locally compact space K as the main example. The study of C_0(K) has been an important area of functional analysis for many years. It gives several new constructions, some involving Boolean rings, of this space as well as many results on the Stonean space of Boolean rings. The book also discusses when Banach spaces of continuous functions are dual spaces and when they are bidual spaces.
GENERALIZED ROSENTHAL'S INEQUALITY FOR BANACH-SPACE-VALUED MARTINGALES
Yu Lin
2009-01-01
A generalized Rosenthal's inequality for Banach-space-valued martingales is proved, which extends the corresponding results in the previous literatures and character-izes the p-uniform smoothness and q-uniform convexity of the underlying Banach space. As an application of this inequality, the strong law of large numbers for Banach-space-valued martingales is also given.
Boundary Controllability of Integrodifferential Systems in Banach Spaces
K Balachandran; E R Anandhi
2001-02-01
Sufficient conditions for boundary controllability of integrodifferential systems in Banach spaces are established. The results are obtained by using the strongly continuous semigroup theory and the Banach contraction principle. Examples are provided to illustrate the theory.
Uniqueness of symmetric basis in quasi-Banach spaces
Albiac, F.; Leránoz, C.
2008-12-01
We show that if X is a nonlocally convex natural quasi-Banach space with symmetric basis whose Banach envelope is isomorphic to l1, then all symmetric bases of X are equivalent. The scope of this result is quite ample since the Banach envelopes of natural quasi-Banach spaces with basis always exhibit an l1-like behavior, in the sense that they contain copies of 's uniformly complemented.
The Topological Degree in Ordered Banach Spaces
Adrian DUMA; Ileana DUMA
2008-01-01
This paper is devoted to the applications of classical topological degrees to nonlinear problems involving various classes of operators acting between ordered Banach spaces. In this frame-work, the Leray-Schauder, Browder-Petryshyn, and Amann-Weiss degree theories are considered, and several existence results are obtained. The non-Archimedean case is also discussed.
Functional Equations in Fuzzy Banach Spaces
M. Eshaghi Gordji
2012-01-01
generalized Hyers-Ulam stability of the following additive-quadratic functional equation f(x+ky+f(x−ky=f(x+y+f(x−y+(2(k+1/kf(ky−2(k+1f(y for fixed integers k with k≠0,±1 in fuzzy Banach spaces.
Generalized mixed equilibrium problem in Banach spaces
Shi-sheng ZHANG
2009-01-01
nsive mappings in a uniformly smooth and strictly convex Banach space.As applications,we utilize our results to study the optimization problem.It shows that our results improve and extend the corresponding results announced by many others recently.
Invariant manifolds for flows in Banach Spaces
Lu Kening.
1989-01-01
The author considers the existence, smoothness and exponential attractivity of global invariant manifolds for flow in Banach Spaces. He shows that every global invariant manifold can be expressed as a graph of a C{sup k} map, provided that the invariant manifolds are exponentially attractive. Applications go to the Reaction-Diffusion equation, the Kuramoto-Sivashinsky equation, and singular perturbed wave equation.
Fixed point theorems for generalized Lipschitzian semigroups in Banach spaces
Balwant Singh Thakur
1999-01-01
Full Text Available Fixed point theorems for generalized Lipschitzian semigroups are proved in p-uniformly convex Banach spaces and in uniformly convex Banach spaces. As applications, its corollaries are given in a Hilbert space, in Lp spaces, in Hardy space Hp, and in Sobolev spaces Hk,p, for 1
A pythagorean approach in Banach spaces
2006-01-01
Full Text Available Let X be a Banach space and S ( X = { x ∈ X , ‖ x ‖ = 1 } be the unit sphere of X . Parameters E ( X = sup { α ( x , x ∈ S ( X } , e ( X = inf { α ( x , x ∈ S ( X } , F ( X = sup { β ( x , x ∈ S ( X } , and f ( X = inf { β ( x , x ∈ S ( X } , where α ( x = sup { ‖ x + y ‖ 2 + ‖ x − y ‖ 2 , y ∈ S ( X } and β ( x = inf { ‖ x + y ‖ 2 + ‖ x − y ‖ 2 , y ∈ S ( X } are introduced and studied. The values of these parameters in the l p spaces and function spaces L p [ 0 , 1 ] are estimated. Among the other results, we proved that a Banach space X with E ( X < 8 , or 2$"> f ( X > 2 is uniform nonsquare; and a Banach space X with E ( X < 5 , or frac{32}{9}$"> f ( X > 32 / 9 has uniform normal structure.
Rank theorems of operators between Banach spaces
2000-01-01
Let E and F be Banach spaces, and B( E, F) all of bounded linear operators on E into F. Let T0 ∈ B( E, F) with an outer inverse T0# ∈ B( F, E). Then a characteristic condition of S= (I + T0# ( T- T0))-1 T0# with T∈ B( E, F) and || T0# ( T- T0) || < 1, being a generalized inverse of T, is presented, and hence, a rank theorem of operators on E into F is established (which generalizes the rank theorem of matrices to Banach spaces). Consequently, an improved finite rank theorem and a new rank theorem are deduced. These results will be very useful to nonlinear functional analysis.
Rank theorems of operators between Banach spaces
无
2000-01-01
Let E and F be Banach spaces, and B(E,F) all of bounded linear operators on E into F. Let T0∈B(E,F) with an outer inverse T#0∈B(F,E). Then a characteristic condition of S=(I+T#0(T-T0))-1T#0 with T∈B(E,F) and ‖T#0(T-T0)‖<1, being a generalized inverse of T, is presented, and hence, a rank theorem of operators on E into F is established (which generalizes the rank theorem of matrices to Banach spaces). Consequently, an improved finite rank theorem and a new rank theorem are deduced. These results will be very useful to nonlinear functional analysis.
Spreading Models in Banach Space Theory
Argyros, S A; Tyros, K
2010-01-01
We extend the classical Brunel-Sucheston definition of the spreading model by introducing the $\\mathcal{F}$-sequences $(x_s)_{s\\in\\mathcal{F}}$ in a Banach space and the plegma families in $\\mathcal{F}$ where $\\mathcal{F}$ is a regular thin family. The new concept yields a transfinite increasing hierarchy of classes of 1-subsymmetric sequences. We explore the corresponding theory and we present examples establishing this hierarchy and illustrating the limitation of the theory.
A General Iterative Method for a Nonexpansive Semigroup in Banach Spaces with Gauge Functions
Kamonrat Nammanee
2012-01-01
Full Text Available We study strong convergence of the sequence generated by implicit and explicit general iterative methods for a one-parameter nonexpansive semigroup in a reflexive Banach space which admits the duality mapping Jφ, where φ is a gauge function on [0,∞. Our results improve and extend those announced by G. Marino and H.-K. Xu (2006 and many authors.
The General Iterative Methods for Asymptotically Nonexpansive Semigroups in Banach Spaces
Rabian Wangkeeree
2012-01-01
Full Text Available We introduce the general iterative methods for finding a common fixed point of asymptotically nonexpansive semigroups which is a unique solution of some variational inequalities. We prove the strong convergence theorems of such iterative scheme in a reflexive Banach space which admits a weakly continuous duality mapping. The main result extends various results existing in the current literature.
Viscosity Approximation Method for Infinitely Many Asymptotically Nonexpansive Maps in Banach Spaces
Ruo Feng RAO
2011-01-01
In the framework of reflexive Banach spaces satisfying a weakly continuous duality map,the author uses the viscosity approximation method to obtain the strong convergence theorem for iterations with infinitely many asymptotically nonexpansive mappings.The main results obtained in this paper improve and extend some recent results.
Irene Benedetti
2015-01-01
Full Text Available We provide existence results for a fractional differential inclusion with nonlocal conditions and impulses in a reflexive Banach space. We apply a technique based on weak topology to avoid any kind of compactness assumption on the nonlinear term. As an example we consider a problem in population dynamic described by an integro-partial-differential inclusion.
Regularization methods for a class of variational inequalities in banach spaces
Buong, Nguyen; Phuong, Nguyen Thi Hong
2012-11-01
In this paper, we introduce two regularization methods, based on the Browder-Tikhonov and iterative regularizations, for finding a solution of variational inequalities over the set of common fixed points of an infinite family of nonexpansive mappings on real reflexive and strictly convex Banach spaces with a uniformly Gateaux differentiate norm.
Integration and differentiation in a Banach space
Gordon, R.A.
1987-01-01
The main focus of the original work in this paper is the extension of Saks's Theory of the Integral to functions that have values in a Banach space. The differentiation of functions that are not of bounded variation and the extension of the Denjoy integral to vector-valued functions are studied in detail. The Riemann integral of functions with values in a Banach space is discussed in detail in an expository chapter. The results of several authors are summarized. The classification of those Banach spaces for which Riemann integrability implies continuity almost everywhere is the highlight of this chapter. Two chapters deal with real-valued functions only. One presents the Denjoy integral while the other discusses the generalized Riemann integral. These chapters provide a good introduction to these integrals. A direct proof that the restricted Denjoy integral is equivalent to the generalized Riemann integral is given. Finally, a brief look at the generalized Riemann integral of vector-valued functions is included. For measurable functions this integral includes both the Pettis integral and the restricted Denjoy-Bochner integral.
Inductive limits and geometry of Banach spaces
Taskinen, Jari
1999-01-01
One of the main problems in the theory of inductive limits of Banach spaces is the projective description problem, finding a reasonable representation for the continuous seminorms. The problem is nontrivial even in the simplest cases. Recall that given, for example, an increasing sequence of Banach spaces (Yk)[infty infinity]k=1 with continuous embeddings Yk[hookrightarrow A: rt arrow-hooked]Yk+1 the inductive limit is the space Y=[cup B: union or logical sum]kYk endowed with the finest locally convex topology [tau] such that every embedding Yk[hookrightarrow A: rt arrow-hooked](Y, [tau]) becomes continuous. It is possible to give abstract definitions for families of continuous seminorms generating the topology [tau], but the connection with the norms of the step spaces Yk is not necessarily very close. For example, if the spaces Yk are Banach spaces of continuous functions endowed with weighted sup-norms, it is not clear if the continuous seminorms of the inductive limit are of the same type.We mention that inductive limits of spaces of continuous and holomorphic functions occur in many areas of analysis like linear partial differential operators, convolution equations [BD1], [E], complex and Fourier analysis and distribution theory. The projective description problem in these spaces has been thoroughly studied in [BMS1, BB1, BB2, BB3, BT, BM1, BM2], to mention some examples. We refer to the survey articles [BM1,BMS2, BB3]. The present work is also connected with the factorization problems which are treated in the book [Ju].
Introduction to Banach spaces and algebras
Allan, Graham
2010-01-01
Banach spaces and algebras are a key topic of pure mathematics. Graham Allan's careful and detailed introductory account will prove essential reading for anyone wishing to specialise in functional analysis and is aimed at final year undergraduates or masters level students. Based on the author's lectures to fourth year students at Cambridge University, the book assumes knowledge typical of first degrees in mathematics, including metric spaces, analytic topology, and complexanalysis. However, readers are not expected to be familiar with the Lebesgue theory of measure and integration.The text be
Spatiality of Derivations of Operator Algebras in Banach Spaces
Quanyuan Chen
2011-01-01
Full Text Available Suppose that A is a transitive subalgebra of B(X and its norm closure A¯ contains a nonzero minimal left ideal I. It is shown that if δ is a bounded reflexive transitive derivation from A into B(X, then δ is spatial and implemented uniquely; that is, there exists T∈B(X such that δ(A=TA−AT for each A∈A, and the implementation T of δ is unique only up to an additive constant. This extends a result of E. Kissin that “if A¯ contains the ideal C(H of all compact operators in B(H, then a bounded reflexive transitive derivation from A into B(H is spatial and implemented uniquely.” in an algebraic direction and provides an alternative proof of it. It is also shown that a bounded reflexive transitive derivation from A into B(X is spatial and implemented uniquely, if X is a reflexive Banach space and A¯ contains a nonzero minimal right ideal I.
Nonuniform exponential unstability of evolution operators in Banach spaces
Megan, Mihail; Sasu, Adina Luminita; Sasu, Bogdan
2001-01-01
In this paper we consider a nonuniform unsrability concept for evolution operators in Banach spaces. The relationship between this concept and the Perron condition is studied. Generalizations to the nonuniform case of some results of Van Minh, Rabiger and Schnaubelt are obtained. The theory we present here is applicable for general time - varying linear equations in Banach spaces.
Phaseless tomographic inverse scattering in Banach spaces
Estatico, C.; Fedeli, A.; Pastorino, M.; Randazzo, A.; Tavanti, E.
2016-10-01
In conventional microwave imaging, a hidden dielectric object under test is illuminated by microwave incident waves and the field it scatters is measured in magnitude and phase in order to retrieve the dielectric properties by solving the related non-homogenous Helmholtz equation or its Lippmann-Schwinger integral formulation. Since the measurement of the phase of electromagnetic waves can be still considered expensive in real applications, in this paper only the magnitude of the scattering wave fields is measured in order to allow a reduction of the cost of the measurement apparatus. In this respect, we firstly analyse the properties of the phaseless scattering nonlinear forward modelling operator in its integral form and we provide an analytical expression for computing its Fréchet derivative. Then, we propose an inexact Newton method to solve the associated nonlinear inverse problems, where any linearized step is solved by a Lp Banach space iterative regularization method which acts on the dual space Lp* . Indeed, it is well known that regularization in special Banach spaces, such us Lp with 1 < p < 2, allows to promote sparsity and to reduce Gibbs phenomena and over-smoothness. Preliminary results concerning numerically computed field data are shown.
Iterative Methods for Pseudocontractive Mappings in Banach Spaces
Jong Soo Jung
2013-01-01
Full Text Available Let E a reflexive Banach space having a uniformly Gâteaux differentiable norm. Let C be a nonempty closed convex subset of E, T:C→C a continuous pseudocontractive mapping with F(T≠∅, and A:C→C a continuous bounded strongly pseudocontractive mapping with a pseudocontractive constant k∈(0,1. Let {αn} and {βn} be sequences in (0,1 satisfying suitable conditions and for arbitrary initial value x0∈C, let the sequence {xn} be generated by xn=αnAxn+βnxn-1+(1-αn-βnTxn, n≥1. If either every weakly compact convex subset of E has the fixed point property for nonexpansive mappings or E is strictly convex, then {xn} converges strongly to a fixed point of T, which solves a certain variational inequality related to A.
Weak* sequential closures in Banach space theory and their applications
Ostrovskii, M. I.
2002-01-01
Let X be a Banach space. Given a subset A of the dual space X* denote by $A_{(1)}$ the weak* sequential closure of A, i.e., the set of all limits of weak*-convergent sequences in A. The study of weak* sequential closures of linear subspaces of the duals of separable Banach spaces was initiated by S.Banach. The first results of this study were presented in the appendix to his book "Theorie des operations lineaires" (1932). It is natural to suppose that the reason for studying weak* sequential ...
Controllability of Impulsive Neutral Functional Differential Inclusions in Banach Spaces
X. J. Wan
2013-01-01
Full Text Available We investigate the controllability of impulsive neutral functional differential inclusions in Banach spaces. Our main aim is to find an effective method to solve the controllability problem of impulsive neutral functional differential inclusions with multivalued jump sizes in Banach spaces. Based on a fixed point theorem with regard to condensing map, sufficient conditions for the controllability of the impulsive neutral functional differential inclusions in Banach spaces are derived. Moreover, a remark is given to explain less conservative criteria for special cases, and work is improved in the previous literature.
Gill, T L [Department of Electrical and Computer Engineering, and Mathematics, Howard University, Washington DC 20059 (United States); Zachary, W W [Department of Electrical and Computer Engineering, Howard University, Washington DC 20059 (United States)], E-mail: tgill@howard.edu, E-mail: wwzachary@earthlink.net
2008-12-12
In this paper, we construct a new class of separable Banach spaces KS{sup p}, for 1 {<=} p {<=} {infinity}, each of which contains all of the standard L{sup p} spaces, as well as the space of finitely additive measures, as compact dense embeddings. Equally important is the fact that these spaces contain all Henstock-Kurzweil integrable functions and, in particular, the Feynman kernel and the Dirac measure, as norm bounded elements. As a first application, we construct the elementary path integral in the manner originally intended by Feynman. We then suggest that KS{sup 2} is a more appropriate Hilbert space for quantum theory, in that it satisfies the requirements for the Feynman, Heisenberg and Schroedinger representations, while the conventional choice only satisfies the requirements for the Heisenberg and Schroedinger representations. As a second application, we show that the mixed topology on the space of bounded continuous functions, C{sub b} [R{sup n} ], used to define the weak generator for a semigroup T(t), is stronger than the norm topology on KS{sup p}. (This means that, when extended to KS{sup p}, T(t) is strongly continuous, so that the weak generator on C{sub b} [R{sup n} ] becomes a strong generator on KS{sup p}.)
Shenghua Wang
2013-01-01
Full Text Available We first introduce the concept of Bregman asymptotically quasinonexpansive mappings and prove that the fixed point set of this kind of mappings is closed and convex. Then we construct an iterative scheme to find a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a countable family of Bregman asymptotically quasinonexpansive mappings in reflexive Banach spaces and prove strong convergence theorems. Our results extend the recent ones of some others.
Open problems in the geometry and analysis of Banach spaces
Guirao, Antonio J; Zizler, Václav
2016-01-01
This is a collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces. Assuming the reader has a working familiarity with the basic results of Banach space theory, the authors focus on concepts of basic linear geometry, convexity, approximation, optimization, differentiability, renormings, weak compact generating, Schauder bases and biorthogonal systems, fixed points, topology and nonlinear geometry. The main purpose of this work is to help convince young researchers in Functional Analysis that the theory of Banach spaces is a fertile field of research, full of interesting open problems. Inside the Banach space area, the text should help expose young researchers to the depth and breadth of the work that remains, and to provide the perspective necessary to choose a direction for further study. Some of the problems presented herein are longstanding open problems, some are recent, some are more important and some are only "local" problems. Some would ...
An explicit construction of sunny nonexpansive retractions in Banach spaces
Simeon Reich
2005-10-01
Full Text Available An explicit algorithmic scheme for constructing the unique sunny nonexpansive retraction onto the common fixed point set of a nonlinear semigroup of nonexpansive mappings in a Banach space is analyzed and a proof of convergence is given.
Third-Order Family of Methods in Banach Spaces
2011-01-24
methods , the latest of which is free of second derivative and it is of third order. In this paper, we use an idea of Kou and Li [Appl. Math . Comp. 187...modified Newton method in Banach space, Appl. Math . Comput. 175 (2006), 1515–1524. [5] L. B. Rall, Computational Solution of Nonlinear Operator...like method in Banach spaces, J. Comp. Appl. Math . 206 (2007), 873–887. [8] V. Candella, A. Marquina, Recurrence relations for rational cubic methods
A Generalization of Uniformly Extremely Convex Banach Spaces
Suyalatu Wulede; Wurichaihu Bai; Wurina Bao
2016-01-01
We discuss a new class of Banach spaces which are the generalization of uniformly extremely convex spaces introduced by Wulede and Ha. We prove that the new class of Banach spaces lies strictly between either the classes of k-uniformly rotund spaces and k-strongly convex spaces or classes of fully k-convex spaces and k-strongly convex spaces and has no inclusive relation with the class of locally k-uniformly convex spaces. We obtain in addition some characterizations and properties of this ne...
Quantitative Hahn-Banach Theorems and Isometric Extensions forWavelet and Other Banach Spaces
Sergey Ajiev
2013-05-01
Full Text Available We introduce and study Clarkson, Dol’nikov-Pichugov, Jacobi and mutual diameter constants reflecting the geometry of a Banach space and Clarkson, Jacobi and Pichugov classes of Banach spaces and their relations with James, self-Jung, Kottman and Schäffer constants in order to establish quantitative versions of Hahn-Banach separability theorem and to characterise the isometric extendability of Hölder-Lipschitz mappings. Abstract results are further applied to the spaces and pairs from the wide classes IG and IG+ and non-commutative Lp-spaces. The intimate relation between the subspaces and quotients of the IG-spaces on one side and various types of anisotropic Besov, Lizorkin-Triebel and Sobolev spaces of functions on open subsets of an Euclidean space defined in terms of differences, local polynomial approximations, wavelet decompositions and other means (as well as the duals and the lp-sums of all these spaces on the other side, allows us to present the algorithm of extending the main results of the article to the latter spaces and pairs. Special attention is paid to the matter of sharpness. Our approach is quasi-Euclidean in its nature because it relies on the extrapolation of properties of Hilbert spaces and the study of 1-complemented subspaces of the spaces under consideration.
Banach frames for multivariate alpha-modulation spaces
Borup, Lasse; Nielsen, Morten
2006-01-01
The α-modulation spaces [$Mathematical Term$], form a family of spaces that include the Besov and modulation spaces as special cases. This paper is concerned with construction of Banach frames for α-modulation spaces in the multivariate setting. The frames constructed are unions of independent Ri...
On the WAε Property and g-NUCε Banach Spaces
FANG Xi-nian; YANG Yi-min
2001-01-01
The WAε property and g-NUCε, g-NUC Banach spaces are introduced. We prove that the WAε property is equivalent to the WBS property and the g-NUCε (resp., g-NUC) spaces are equivalent to the NUCε (resp., NUC) spaces possessing the BS property. So we obtain a characterization of the NUCε (resp. , NUC) spaces possessing the BS property.
Calculus Rules for V-Proximal Subdifferentials in Smooth Banach Spaces
Messaoud Bounkhel
2016-01-01
Full Text Available In 2010, Bounkhel et al. introduced new proximal concepts (analytic proximal subdifferential, geometric proximal subdifferential, and proximal normal cone in reflexive smooth Banach spaces. They proved, in p-uniformly convex and q-uniformly smooth Banach spaces, the density theorem for the new concepts of proximal subdifferential and various important properties for both proximal subdifferential concepts and the proximal normal cone concept. In this paper, we establish calculus rules (fuzzy sum rule and chain rule for both proximal subdifferentials and we prove the Bishop-Phelps theorem for the proximal normal cone. The limiting concept for both proximal subdifferentials and for the proximal normal cone is defined and studied. We prove that both limiting constructions coincide with the Mordukhovich constructions under some assumptions on the space. Applications to nonconvex minimisation problems and nonconvex variational inequalities are established.
Construction of generalized atomic decompositions in Banach spaces
Raj Kumar
2014-06-01
Full Text Available G-atomic decompositions for Banach spaces with respect to a model space of sequences have been introduced and studied as a generalization of atomic decompositions. Examples and counter example have been provided to show its existence. It has been proved that an associated Banach space for G-atomic decomposition always has a complemented subspace. The notion of a representation system is introduced and exhibits its relation with G-atomic decomposition. Also It has been observed that G-atomic decompositions are exactly compressions of Schauder decompositions for a larger Banach space. We give a characterization for finite G-atomic decomposition in terms of finite-dimensional expansion of identity. Keywords: complemented coefficient spaces, finite-dimensional expansion of identity, G-atomic decomposition, representation system.
Metric embeddings bilipschitz and coarse embeddings into Banach spaces
Ostrovskii, Mikhail I
2013-01-01
Embeddings of discrete metric spaces into Banach spaces recently became an important tool in computer science and topology. The book will help readers to enter and to work in this very rapidly developing area having many important connections with different parts of mathematics and computer science. The purpose of the book is to present some of the most important techniques and results, mostly on bilipschitz and coarse embeddings. The topics include embeddability of locally finite metric spaces into Banach spaces is finitely determined, constructions of embeddings, distortion in terms of Poinc
Atomic decompositions of Banach-space-valued martingales
刘培德; 侯友良
1999-01-01
Several theorems for atomic decompositions of Banach-space-valued martingales are proved. As their applications, the relationship among some martingale spaces such as H_α(X) and _ρ(?)_α in the case 0<α≤1 are studied. It is shown that there is a close connection between the results and the smoothness and convexity of the value spaces.
Bashir Ali
2012-01-01
Full Text Available Let be a real reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm. Let ={(∶≥0} be a family of uniformly asymptotically regular generalized asymptotically nonexpansive semigroup of , with functions ,∶[0,∞→[0,∞. Let ∶=(=∩≥0((≠∅ and ∶→ be a weakly contractive map. For some positive real numbers and satisfying +>1, let ∶→ be a -strongly accretive and -strictly pseudocontractive map. Let {} be an increasing sequence in [0,∞ with lim→∞=∞, and let {} and {} be sequences in (0,1] satisfying some conditions. Strong convergence of a viscosity iterative sequence to common fixed points of the family of uniformly asymptotically regular asymptotically nonexpansive semigroup, which also solves the variational inequality ⟨(−,(−⟩≤0, for all ∈, is proved in a framework of a real Banach space.
A Decomposition of the Dual Space of Some Banach Function Spaces
Claudia Capone
2012-01-01
Full Text Available We give a decomposition for the dual space of some Banach Function Spaces as the Zygmund space EXP of the exponential integrable functions, the Marcinkiewicz space ,∞, and the Grand Lebesgue Space ,.
On well posedness of best simultaneous approximation problems in Banach spaces
LI; Chong
2001-01-01
［1］Pinkus, A., Uniqueness in vector-valued approximation, J. Approx. Theory, 1993, 73: 17—92.［2］Li, C., Watson, G. A., On best simultaneous approximation, J. Approx. Theory, 1997, 91: 332—348.［3］Tanimoto, S., A characterization of best simultaneous approximations, J. Approx. Theory, 1989, 59: 359—361.［4］Watson, G. A., A characterization of best simultaneous approximations, J. Approx. Theory, 1993, 75: 175—182.［5］Li, C., Watson, G. A., On best simultaneous approximation of a finite set of functions, Computer Math. Applic., 1999, 37: 1—9.［6］Stechkin, S. B., Approximation properties of sets in normed linear spaces, Rev. Roumaine Math. Pures and Appl. (in Russian), 1963, 8: 5—18.［7］Borwein, J. M., Fitzpatrick, S., Existence of nearest points in Banach spaces, Can. J. Math., 1989, 41: 702—720.［8］De Blasi, F. S., Myjak, J., On a generalized best approximation problem, J. Approx. Theory, 1998, 94: 54—72.［9］Georgiev, P. G., The strong Ekeland variational principle, the strong drop theorem and applications, J. Math. Anal. Appl., 1988, 131: 1—21.［10］Lau, K. S., Almost Chebyshev subsets in reflexive Banach spaces, Indiana Univ. Math. J., 1978, 27: 791—795.［11］Li, C., On mutually nearest and mutually furthest points in reflexive Banach spaces, J. Approx. Theory, 2000, 103: 1—17.［12］Li, C., On well posed generalized best approximation problems, J. Approx. Thory, 2000, 107: 96—108.［13］Li, C., Almost K-Chebyshev sets, Acta. Math. Sin. (in Chinese), 1990, 33: 251—259.［14］De Blasi, F. S., Myjak, J., Papini, P. L., On mutually nearest and mutually furthest points of sets in Banach spaces, J. Approx. Theory, 1992, 70: 142—155.［15］Dontchev, A., Zolezzi, T., Well Posed Optimization Problems, Lecture Notes in Math., Vol. 1543, New York: Springer-Verlag, 1993.［16］Li, C., Wang, X. H., Almost Chebyshev set with respect to bounded subsets, Science in China, Ser. A, 1997, 40: 375—383.［17］Ni, R
Properties of Toeplitz Operators on Some Holomorphic Banach Function Spaces
Ahmed El-Sayed Ahmed
2012-01-01
Full Text Available We characterize complex measures on the unit ball of ℂ, for which the general Toeplitz operator is bounded or compact on the analytic Besov spaces (, also on the minimal Möbius invariant Banach spaces 1( in the unit ball .
Phillips' Lemma for L-embedded Banach spaces
Pfitzner, Hermann
2010-01-01
In this note the following version of Phillips' lemma is proved. The L-projection of an L-embedded space - that is of a Banach space which is complemented in its bidual such that the norm between the two complementary subspaces is additive - is weak-weakly sequentially continuous.
Riesz Isomorphisms of Tensor Products of Order Unit Banach Spaces
T S S R K Rao
2009-06-01
In this paper we formulate and prove an order unit Banach space version of a Banach–Stone theorem type theorem for Riesz isomorphisms of the space of vector-valued continuous functions. Similar results were obtained recently for the case of lattice-valued continuous functions in [5] and [6].
Locally uniformly convex norms in Banach spaces and their duals
Haydon, Richard
2006-01-01
It is shown that a Banach space with locally uniformly convex dual admits an equivalent norm which is itself locally uniformly convex. It follows that on any such space all continuous real-valued functions may be uniformly approximated by C^1 functions.
Bounded cohomology with coefficients in uniformly convex Banach spaces
Bestvina, Mladen; Bromberg, Ken; Fujiwara, Koji
2013-01-01
We show that for acylindrically hyperbolic groups $\\Gamma$ (with no nontrivial finite normal subgroups) and arbitrary unitary representation $\\rho$ of $\\Gamma$ in a (nonzero) uniformly convex Banach space the vector space $H^2_b(\\Gamma;\\rho)$ is infinite dimensional. The result was known for the regular representations on $\\ell^p(\\Gamma)$ with $1
A Banach Space Regularization Approach for Multifrequency Microwave Imaging
Claudio Estatico
2016-01-01
Full Text Available A method for microwave imaging of dielectric targets is proposed. It is based on a tomographic approach in which the field scattered by an unknown target (and collected in a proper observation domain is inverted by using an inexact-Newton method developed in Lp Banach spaces. In particular, the extension of the approach to multifrequency data processing is reported. The mathematical formulation of the new method is described and the results of numerical simulations are reported and discussed, analyzing the behavior of the multifrequency processing technique combined with the Banach spaces reconstruction method.
Approximating stationary points of stochastic optimization problems in Banach space
Balaji, Ramamurthy; Xu, Huifu
2008-11-01
In this paper, we present a uniform strong law of large numbers for random set-valued mappings in separable Banach space and apply it to analyze the sample average approximation of Clarke stationary points of a nonsmooth one stage stochastic minimization problem in separable Banach space. Moreover, under Hausdorff continuity, we show that with probability approaching one exponentially fast with the increase of sample size, the sample average of a convex compact set-valued mapping converges to its expected value uniformly. The result is used to establish exponential convergence of stationary sequence under some metric regularity conditions.
Banach spaces and descriptive set theory selected topics
Dodos, Pandelis
2010-01-01
This volume deals with problems in the structure theory of separable infinite-dimensional Banach spaces, with a central focus on universality problems. This topic goes back to the beginnings of the field and appears in Banach's classical monograph. The novelty of the approach lies in the fact that the answers to a number of basic questions are based on techniques from Descriptive Set Theory. Although the book is oriented on proofs of several structural theorems, in the main text readers will also find a detailed exposition of numerous “intermediate” results which are interesting in their own right and have proven to be useful in other areas of Functional Analysis. Moreover, several well-known results in the geometry of Banach spaces are presented from a modern perspective.
THE MINIMAL PROPERTY OF THE CONDITION NUMBER OF INVERTIBLE LINEAR BOUNDED OPERATORS IN BANACH SPACES
陈果良; 魏木生
2002-01-01
In this paper we show that in error estimates, the condition number κ(T) of any invertible linear bounded operator T in Banach spaces is minimal. We also extend the Hahn-Banach theorem and other related results.
Stochastic Integration in Banach Spaces using a product structure with partial order
Bierkens, Joris
2009-01-01
Using a multiplicative structure (for example that of a Banach algebra) and a partial order we construct a weak version of a Banach space valued stochastic integral with respect to square integrable martingales.
MULTI-VALUED QUASI VARLATIONAL INCLUSIONS IN BANACH SPACES
张石生
2004-01-01
The purpose is to introduce and study a class of more general multivalued quasi variational inclusions in Banach spaces.By using the resolvent operator technique some existence theorem of solutions and iterative approximation for solving this kind of multivalued quasi variational inclusions are established.The results generalize,improve and unify a number of Noor's and others' recent results.
A NOTE ON REARRANGEMENTS OF SERIES IN BANACH SPACES
ZhongHuaijie
1994-01-01
We generalize Kadec's and Yan Zikun's resuhs in [1],[2] to prove; in every infinite dimensional real Banach space Y there exist an infinite dimensional subspace X and a series ∑xn such that ∑xn has property(N) in X. but(the domain of sums of this series) S(∑xn) is not a convex set.
The reconstruction property in Banach spaces and a perturbation theorem
Casazza, P.G.; Christensen, Ole
2008-01-01
Perturbation theory is a fundamental tool in Banach space theory. However, the applications of the classical results are limited by the fact that they force the perturbed sequence to be equivalent to the given sequence. We will develop a more general perturbation theory that does not force...
The reconstruction property in Banach spaces and a perturbation theorem
Casazza, P.G.; Christensen, Ole
2008-01-01
Perturbation theory is a fundamental tool in Banach space theory. However, the applications of the classical results are limited by the fact that they force the perturbed sequence to be equivalent to the given sequence. We will develop a more general perturbation theory that does not force equiva...
Viscosity Approximation Methods for Two Accretive Operators in Banach Spaces
Jun-Min Chen
2013-01-01
Full Text Available We introduced a viscosity iterative scheme for approximating the common zero of two accretive operators in a strictly convex Banach space which has a uniformly Gâteaux differentiable norm. Some strong convergence theorems are proved, which improve and extend the results of Ceng et al. (2009 and some others.
Mann Iteration of Weak Convergence Theorems in Banach Space
Liang-gen Hu; Jin-ping Wang
2009-01-01
In this paper, by using Mann's iteration process we will establish several weak convergence theorems for approximating a fixed point of κ-strictly pseudocontractive mappings with respect to p in p-uniformly convex Banach spaces. Our results answer partially the open question proposed by Marino and Xu, and extend Reich's theorem from nonexpausive mappings to κ-strict pseudocontractive mappings.
On the uniqueness of minimal projections in Banach spaces
Ewa Szlachtowska
2012-01-01
Full Text Available Let \\(X\\ be a uniformly convex Banach space with a continuous semi-inner product. We investigate the relation of orthogonality in \\(X\\ and generalized projections acting on \\(X\\. We prove uniqueness of orthogonal and co-orthogonal projections.
Continuous local martingales and stochastic integration in UMD Banach spaces
Veraar, M.C.
2007-01-01
Recently, van Neerven, Weis and the author, constructed a theory for stochastic integration of UMD Banach space valued processes. Here the authors use a (cylindrical) Brownian motion as an integrator. In this note we show how one can extend these results to the case where the integrator is an arbitr
Convergence on Composite Iterative Schemes for Nonexpansive Mappings in Banach Spaces
Jung JongSoo
2008-01-01
Full Text Available Abstract Let be a reflexive Banach space with a uniformly Gâteaux differentiable norm. Suppose that every weakly compact convex subset of has the fixed point property for nonexpansive mappings. Let be a nonempty closed convex subset of , a contractive mapping (or a weakly contractive mapping, and nonexpansive mapping with the fixed point set . Let be generated by a new composite iterative scheme: , , . It is proved that converges strongly to a point in , which is a solution of certain variational inequality provided that the sequence satisfies and , for some and the sequence is asymptotically regular.
Jeribi, Aref
2015-01-01
Uncover the Useful Interactions of Fixed Point Theory with Topological StructuresNonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications is the first book to tackle the topological fixed point theory for block operator matrices with nonlinear entries in Banach spaces and Banach algebras. The book provides researchers and graduate students with a unified survey of the fundamental principles of fixed point theory in Banach spaces and algebras. The authors present several exten
Ofoedu EU
2008-01-01
Full Text Available Abstract Let be a real reflexive and strictly convex Banach space which has a uniformly Gâteaux differentiable norm and be a closed convex nonempty subset of . Strong convergence theorems for approximation of a common zero of a countably infinite family of -accretive mappings from to are proved. Consequently, we obtained strong convergence theorems for a countably infinite family of pseudocontractive mappings.
E. U. Ofoedu
2008-03-01
Full Text Available Let E be a real reflexive and strictly convex Banach space which has a uniformly GÃƒÂ¢teaux differentiable norm and C be a closed convex nonempty subset of E. Strong convergence theorems for approximation of a common zero of a countably infinite family of m-accretive mappings from C to E are proved. Consequently, we obtained strong convergence theorems for a countably infinite family of pseudocontractive mappings.
Integrals and Banach spaces for finite order distributions
Talvila, Erik
2011-01-01
Let $\\Bc$ denote the real-valued functions continuous on the extended real line and vanishing at $-\\infty$. Let $\\Br$ denote the functions that are left continuous, have a right limit at each point and vanish at $-\\infty$. Define $\\acn$ to be the space of tempered distributions that are the $n$th distributional derivative of a unique function in $\\Bc$. Similarly with $\\arn$ from $\\Br$. A type of integral is defined on distributions in $\\acn$ and $\\arn$. The multipliers are iterated integrals of functions of bounded variation. For each $n\\in\\N$, the spaces $\\acn$ and $\\arn$ are Banach spaces, Banach lattices and Banach algebras isometrically isomorphic to $\\Bc$ and $\\Br$, respectively. Under the ordering in this lattice, if a distribution is integrable then its absolute value is integrable. The dual space is isometrically isomorphic to the functions of bounded variation. The space $\\ac^1$ is the completion of the $L^1$ functions in the Alexiewicz norm. The space $\\ar^1$ contains all finite signed Borel measure...
Geometric properties of Banach spaces and nonlinear iterations
Chidume, Charles
2009-01-01
Nonlinear functional analysis and applications is an area of study that has provided fascination for many mathematicians across the world. This monograph delves specifically into the topic of the geometric properties of Banach spaces and nonlinear iterations, a subject of extensive research over the past thirty years. Chapters 1 to 5 develop materials on convexity and smoothness of Banach spaces, associated moduli and connections with duality maps. Key results obtained are summarized at the end of each chapter for easy reference. Chapters 6 to 23 deal with an in-depth, comprehensive and up-to-date coverage of the main ideas, concepts and results on iterative algorithms for the approximation of fixed points of nonlinear nonexpansive and pseudo-contractive-type mappings. This includes detailed workings on solutions of variational inequality problems, solutions of Hammerstein integral equations, and common fixed points (and common zeros) of families of nonlinear mappings. Carefully referenced and full of recent,...
S-Mixing Tuple of Operators on Banach Spaces
Wei Wang
2016-01-01
Full Text Available We consider the question: what is the appropriate formulation of Godefroy-Shapiro criterion for tuples of operators? We also introduce a new notion about tuples of operators, S-mixing, which lies between mixing and weakly mixing. We also obtain a sufficient condition to ensure a tuple of operators to be S-mixing. Moreover, we study some new properties of S-mixing operators on several concrete Banach spaces.
Some Properties of the Injective Tensor Product of Banach Spaces
Xiao Ping XUE; Yong Jin LI; Qing Ying BU
2007-01-01
Let X and Y be Banach spaces such that X has an unconditional basis. Then X?Y, the injective tensor product of X and Y, has the Radon-Nikodym property (respectively, the analytic Radon-Nikodym property, the near Radon-Nikodym property, non-containment of a copy of co, weakly sequential completeness) if and only if both X and Y have the same property and each continuous linear operator from the predual of X to Y is compact.
ISHIKAWA ITERATIVE PROCESS IN UNIFORMLY SMOOTH BANACH SPACES
黄震宇
2001-01-01
Let E be a uniformly smooth Banach space, K be a nonempty closed convex subset of E, and suppose: T: K → K is a continuous φ-strongly pseudocontractive operator with a bounded range. Using a new analytical method, under general cases, the Ishikawa iterative process { xn } converges strongly to the unique fixed point x * of the operator Twere proved. The paper generalizes and extends a lot of recent corresponding results.
New iterative schemes for asymptotically quasi-nonexpansive nonself-mappings in Banach spaces
Wang, Chao; Zhu, Jinghao; An, Lili
2010-04-01
In this paper, a new two-step iterative scheme with errors is introduced for two asymptotically quasi-nonexpansive nonself-mappings. Several convergence theorems are established in real Banach spaces and real uniformly convex Banach spaces. Our theorems improve and extend the results due to Thianwan [S. Thianwan, Common fixed point of new iterations for two asymptotically nonexpansive nonself-mappings in a Banach space, J. Comput. Appl. Math. 224 (2009) 685-695] and many other papers.
The Hilbert Inequality in Banach Spaces%Banach空间上的Hilbert不等式
华柳斌; 黎永锦
2011-01-01
Some Hilbert's inequalities in Hilbert spaces and Banach spaces were discussed by inner and functional. The Hilbert spaces and Banach space version of Hilbert's inequalities were established.%利用内积和泛函,在Hilbert空间和Banach空间中讨论Hilbert不等式,建立了抽象空间的Hilbert不等式.
A proximal point method for nonsmooth convex optimization problems in Banach spaces
Y. I. Alber
1997-01-01
Full Text Available In this paper we show the weak convergence and stability of the proximal point method when applied to the constrained convex optimization problem in uniformly convex and uniformly smooth Banach spaces. In addition, we establish a nonasymptotic estimate of convergence rate of the sequence of functional values for the unconstrained case. This estimate depends on a geometric characteristic of the dual Banach space, namely its modulus of convexity. We apply a new technique which includes Banach space geometry, estimates of duality mappings, nonstandard Lyapunov functionals and generalized projection operators in Banach spaces.
Vittorio Colao
2012-01-01
Full Text Available We prove the equivalence and the strong convergence of iterative processes involving generalized strongly asymptotically -pseudocontractive mappings in uniformly smooth Banach spaces.
Greedy Algorithms for Reduced Bases in Banach Spaces
DeVore, Ronald
2013-02-26
Given a Banach space X and one of its compact sets F, we consider the problem of finding a good n-dimensional space X n⊂X which can be used to approximate the elements of F. The best possible error we can achieve for such an approximation is given by the Kolmogorov width dn(F)X. However, finding the space which gives this performance is typically numerically intractable. Recently, a new greedy strategy for obtaining good spaces was given in the context of the reduced basis method for solving a parametric family of PDEs. The performance of this greedy algorithm was initially analyzed in Buffa et al. (Modél. Math. Anal. Numér. 46:595-603, 2012) in the case X=H is a Hilbert space. The results of Buffa et al. (Modél. Math. Anal. Numér. 46:595-603, 2012) were significantly improved upon in Binev et al. (SIAM J. Math. Anal. 43:1457-1472, 2011). The purpose of the present paper is to give a new analysis of the performance of such greedy algorithms. Our analysis not only gives improved results for the Hilbert space case but can also be applied to the same greedy procedure in general Banach spaces. © 2013 Springer Science+Business Media New York.
Density of a semigroup in a Banach space
Borodin, P. A.
2014-12-01
We study conditions on a set M in a Banach space X which are necessary or sufficient for the set R(M) of all sums x_1+\\dots+x_n, x_k\\in M, to be dense in X. We distinguish conditions under which the closure \\overline{R(M)} is an additive subgroup of X, and conditions under which this additive subgroup is dense in X. In particular, we prove that if M is a closed rectifiable curve in a uniformly convex and uniformly smooth Banach space X, and does not lie in a closed half-space \\{x\\in X\\colon f(x)≥0\\}, f\\in X^*, and is minimal in the sense that every proper subarc of M lies in an open half-space \\{x\\in X\\colon f(x)>0\\}, then \\overline{R(M)}=X. We apply our results to questions of approximation in various function spaces.
Ito's formula in UMD Banach spaces and regularity of solution of the Zakai equation
Brzezniak, Z.; Van Neerven, J.M.A.M.; Veraar, M.C.; Weis, L.
2008-01-01
Using the theory of stochastic integration for processes with values in a UMD Banach space developed recently by the authors, an Itô formula is proved which is applied to prove the existence of strong solutions for a class of stochastic evolution equations in UMD Banach spaces. The abstract results
A New Iterative Scheme of Modified Mann Iteration in Banach Space
Jinzuo Chen
2014-01-01
Full Text Available We introduce the modified iterations of Mann's type for nonexpansive mappings and asymptotically nonexpansive mappings to have the strong convergence in a uniformly convex Banach space. We study approximation of common fixed point of asymptotically nonexpansive mappings in Banach space by using a new iterative scheme. Applications to the accretive operators are also included.
Strict property (M) in Banach spaces
Cui, Yunan
1999-01-01
A new property, namely strict property $(M)$, that implies the Opial property is introduced. We discuss relations between this property and some other well known properties. We also prove that Cesaro sequence spaces have strict property $(M)$.
Maximal regularity of second order delay equations in Banach spaces
无
2010-01-01
We give necessary and sufficient conditions of Lp-maximal regularity(resp.B sp ,q-maximal regularity or F sp ,q-maximal regularity) for the second order delay equations:u″(t)=Au(t) + Gu’t + F u t + f(t), t ∈ [0, 2π] with periodic boundary conditions u(0)=u(2π), u′(0)=u′(2π), where A is a closed operator in a Banach space X,F and G are delay operators on Lp([-2π, 0];X)(resp.Bsp ,q([2π, 0];X) or Fsp,q([-2π, 0;X])).
FRAME MULTIRESOLUTION ANALYSIS AND INFINITE TREES IN BANACH SPACES ON LOCALLY COMPACT ABELIAN GROUPS
S. S. Panday
2004-01-01
We extend the concept of frame multiresolution analysis to a locally compact abelian group and use it to define certain weighted Banach spaces and the spaces of their antifunctionals. We define analysis and synthesis operators on these spaces and establish the continuity of their composition. Also, we prove a general result to characterize infinite trees in the above Banach spaces of antifunctionals. This paper paves the way for the study of corresponding problems associated with some other types of Banach spaces on locally compact abelian groups including modulation spaces.
Yekini SHEHU
2014-01-01
Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gˆateaux differentiable norm. Assume that every nonempty closed con-vex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive map-pings which is also a unique solution to variational inequality problem involving φ-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, con-vex optimization problems, and split feasibility problems. Our result extends many recent important results.
Fixed point variational solutions for uniformly continuous pseudocontractions in banach spaces
2006-01-01
Full Text Available Let E be a reflexive Banach space with a uniformly Gâteaux differentiable norm, let K be a nonempty closed convex subset of E , and let T:K→K be a uniformly continuous pseudocontraction. If f:K→K is any contraction map on K and if every nonempty closed convex and bounded subset of K has the fixed point property for nonexpansive self-mappings, then it is shown, under appropriate conditions on the sequences of real numbers { α n } , { μ n } , that the iteration process z 1 ∈K , z n+1 = μ n ( α n T z n +( 1− α n z n +( 1− μ n f( z n , n∈ℕ , strongly converges to the fixed point of T , which is the unique solution of some variational inequality, provided that K is bounded.
Yali Li
2008-01-01
Full Text Available Let K be a nonempty closed convex subset of a reflexive and strictly convex Banach space E with a uniformly Gâteaux differentiable norm, ℱ={T(h:h≥0} a generalized asymptotically nonexpansive self-mapping semigroup of K, and f:K→K a fixed contractive mapping with contractive coefficient β∈(0,1. We prove that the following implicit and modified implicit viscosity iterative schemes {xn} defined by xn=αnf(xn+(1−αnT(tnxn and xn=αnyn+(1−αnT(tnxn, yn=βnf(xn−1+(1−βnxn−1 strongly converge to p∈F as n→∞ and p is the unique solution to the following variational inequality: 〈f(p−p,j(y−p〉≤0 for all y∈F.
On strictly singular operators between separable Banach spaces
Beanland, Kevin
2010-01-01
Let $X$ and $Y$ be separable Banach spaces and denote by $\\sss\\sss(X,Y)$ the subset of $\\llll(X,Y)$ consisting of all strictly singular operators. We study various ordinal ranks on the set $\\sss\\sss(X,Y)$. Our main results are summarized as follows. Firstly, we define a new rank $\\rs$ on $\\sss\\sss(X,Y)$. We show that $\\rs$ is a co-analytic rank and that dominates the rank $\\varrho$ introduced by Androulakis, Dodos, Sirotkin and Troitsky [Israel J. Math., 169 (2009), 221-250]. Secondly, for every $1\\leq p<+\\infty$ we construct a Banach space $Y_p$ with an unconditional basis such that $\\sss\\sss(\\ell_p, Y_p)$ is a co-analytic non-Borel subset of $\\llll(\\ell_p,Y_p)$ yet every strictly singular operator $T:\\ell_p\\to Y_p$ satisfies $\\varrho(T)\\leq 2$. This answers a question of Argyros.
Homomorphisms and functional calculus on algebras on entire functions on Banach spaces
H. M. Pryimak
2015-07-01
Full Text Available The paper is devoted to study homomorphisms of algebras of entire functionson Banach spaces to a commutative Banach algebra. In particular, it is proposed amethod to construct homomorphisms vanishing on homogeneouspolynomials of degree less or equal that a fixed number $n.$
Coupling and Strong Feller for Jump Processes on Banach Spaces
Wang, Feng-Yu
2011-01-01
By using lower bound conditions of the L\\'evy measure w.r.t. a nice reference measure, the coupling and strong Feller properties are investigated for the Markov semigroup associated with a class of linear SDEs driven by (non-cylindrical) L\\'evy processes on a Banach space. Unlike in the finite-dimensional case where these properties have also been confirmed for L\\'evy processes without drift, in the infinite-dimensional setting the appearance of a drift term is essential to ensure the quasi-invariance of the process by shifting the initial data. Gradient estimates and exponential convergence are also investigated. The main results are illustrated by specific models on the Wiener space and separable Hilbert spaces.
Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces
Lindenstrauss, Joram; Tiaer, Jaroslav
2012-01-01
This book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. Because the question turns out to be closely related to porous sets in Banach spaces, it provides a bridge between descriptive set theory and the classical topic of existence of derivatives of vector-valued Lipschitz functions. The topic is relevant to classical analysis and descriptive set theory on Banach spaces. The book opens several new research directions in this area of geometric nonlinear functional analysi
Remarks on quasi-isometric non-embeddability into uniformly convex Banach spaces
Nowak, Piotr W.
2005-01-01
We construct a locally finite graph and a bounded geometry metric space which do not admit a quasi-isometric embedding into any uniformly convex Banach space. Connections with the geometry of $c_0$ and superreflexivity are discussed.
Generalized Browder's and Weyl's theorems for Banach space operators
Curto, Raúl E.; Han, Young Min
2007-12-01
We find necessary and sufficient conditions for a Banach space operator T to satisfy the generalized Browder's theorem. We also prove that the spectral mapping theorem holds for the Drazin spectrum and for analytic functions on an open neighborhood of [sigma](T). As applications, we show that if T is algebraically M-hyponormal, or if T is algebraically paranormal, then the generalized Weyl's theorem holds for f(T), where f[set membership, variant]H((T)), the space of functions analytic on an open neighborhood of [sigma](T). We also show that if T is reduced by each of its eigenspaces, then the generalized Browder's theorem holds for f(T), for each f[set membership, variant]H([sigma](T)).
Stochastic integration in Banach spaces theory and applications
Mandrekar, Vidyadhar
2015-01-01
Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces. The book is intended for graduate students and researchers in stochastic (partial) differential equations, mathematical finance and non-linear filtering and assumes a knowledge of the required integrati...
Yan Tang
2013-01-01
Full Text Available Suppose that C is a nonempty closed convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. A viscosity iterative process is constructed in this paper. A strong convergence theorem is proved for a common element of the set of fixed points of a finite family of pseudocontractive mappings and the set of solutions of a finite family of monotone mappings. And the common element is the unique solution of certain variational inequality. The results presented in this paper extend most of the results that have been proposed for this class of nonlinear mappings.
A SUPER-HALLEY TYPE APPROXIMATION IN BANACH SPACES
J.A. Ezquerro; M.A. Hernández
2001-01-01
The Super-Halley method is one of the best known third-orderiteration for solving nonlinear equations. A Newton-like method which is an approximation of this method is studied. Our approach yields a fourth R-order iterative process which is more efficient than its classical predecessor. We establish a Newton-Kantorovich-type convergence theorem using a new system of recurrence relations, and give an explicit expression for the a priori error bounds of the iteration.CLC Number：O17 Document ID：AAuthor Resume：J.A. Ezquerro,e-mail : jezquer@siur. unirioja. es mahernan@siur. unirioja. es References：[1]Argyros,I.K. ,Chen,D. andQian,Q. ,An Inverse-Free Jarratt Type Approximation in a Banach Space,J. Appr. Th. Appl.,12(1996),No. 1,19-30.[2]Argyros,I. K. ,Chen,D. And Qian,Q. ,The Jarratt Method in Banach Space Setting,J.Comput. Appl. Math.,51(1994),103-106.[3]Candela,V. And Marquina,A. ,Recurrence Relations for Rational Cubic Methods I: The Halley Method,Computing,44(1990),169- 184.[4]Candela,V. And Marquina,A. ,Recurrence Relations for Rational Cubic Method I : TheChebyshev Method,Computing,45(1990),355-[3]67.[5]Chen,D.,Argyros,I.K.andQian,Q.,ALocalConvergenceTheoremfortheSuper-HalleyMethodinaBanachSpace,Appl.Math.Lett.,7(1994),No.5,49-52.[6]Hernández,M.A.,Newton-Raphson'sMethodandConvexity,Zb.Rad.Prirod.Mat.Fak.Ser.Mat.,22(1992),No.1,1591-66.[7]Kantorovich,L.V.,TheMajorantPrincipleforNewton'sMethod,Dokl.Akad.Nauk,SSSR,76(1951),17-20.[8]Potra,F.A.adnPták,V.,NondiscreteInductionandIterativeProcesses,Pitman,NewYork,1984.[9]Rall,L.B.,ComputationalSolutionofNonlinearOperatorEquations,JohnWiley&-Sons,NewYork,1979.[10]Safiev,R.A.,OnSomeIterativeProcesses,Z,Vyccisl.Mat.Fiz.,4,193-143(TranslatedintoEnglishbyL.B.RallasMRCTechnicalSummaryReport,No.649,Univ.Wisconsin-Madison,1966).Manuscript Received：1998年10月20日Published：2001年9月1日
Kim JongKyu
2009-01-01
Full Text Available We study the strong convergence of two kinds of viscosity iteration processes for approximating common fixed points of the pseudocontractive semigroup in uniformly convex Banach spaces with uniformly Gâteaux differential norms. As special cases, we get the strong convergence of the implicit viscosity iteration process for approximating common fixed points of the nonexpansive semigroup in Banach spaces satisfying some conditions. The results presented in this paper extend and generalize some results concerned with the nonexpansive semigroup in (Chen and He, 2007 and the pseudocontractive mapping in (Zegeye et al., 2007 to the pseudocontractive semigroup in Banach spaces under different conditions.
Porous sets for mutually nearest points in Banach spaces
Chong Li
2008-01-01
Full Text Available Let \\(\\mathfrak{B}(X\\ denote the family of all nonempty closed bounded subsets of a real Banach space \\(X\\, endowed with the Hausdorff metric. For \\(E, F \\in \\mathfrak{B}(X\\ we set \\(\\lambda_{EF} = \\inf \\{\\|z - x\\| : x \\in E, z \\in F \\}\\. Let \\(\\mathfrak{D}\\ denote the closure (under the maximum distance of the set of all \\((E, F \\in \\mathfrak{B}(X \\times \\mathfrak{B}(X\\ such that \\(\\lambda_{EF} \\gt 0\\. It is proved that the set of all \\((E, F \\in \\mathfrak{D}\\ for which the minimization problem \\(\\min_{x \\in E, z\\in F}\\|x - z\\|\\ fails to be well posed in a \\(\\sigma\\-porous subset of \\(\\mathfrak{D}\\.
A New Class of Banach Spaces with Uniform Normal Structure
GAO Ji
2001-01-01
Let X be a Banach space, S (X) be the unit sphere of X, ψ be a function: S ( X)→ S ( X * )such that ψ(x)∈ x, and vψ(ε)=inf ,0 ≤ ε ≤ 2, where x is the set of norm 1 supporting functionals of S (X) at x. A geometric concept,modulus of V-convexity V(ε) = sup{ Vψ(ε), for all ψ: S(X)→ S(X* )}, is introduced; the properties of V( ε ) and the relationship between V(ε ) and other geometric concepts are discussed. The main result is that V(1/2)＞0 implies normal structure.
Banach spaces without approximation properties of type p
Reinov, Oleg
2010-01-01
The main purpose of this note is to show that the question posed in the paper of Sinha D.P. and Karn A.K.("Compact operators which factor through subspaces of $l_p$ Math. Nachr. 281, 2008, 412-423; see the very end of that paper) has a negative answer, and that the answer was known, essentially, in 1985 after the papers "Approximation properties of order p and the existence of non-p-nuclear operators with p-nuclear second adjoints" (Math. Nachr. 109(1982), 125-134) and "Approximation of operators in Banach spaces" (Application of functional analysis in the approximation theory (KGU, Kalinin), 1985, 128-142) by Reinov O.I. have been appeared in 1982 and in 1985 respectively.
Strong convergence theorems for maximal monotone mappings in Banach spaces
Zegeye, Habtu
2008-07-01
Let E be a uniformly convex and 2-uniformly smooth real Banach space with dual E*. Let be a Lipschitz continuous monotone mapping with A-1(0)[not equal to][empty set]. For given u,x1[set membership, variant]E, let {xn} be generated by the algorithm xn+1:=[beta]nu+(1-[beta]n)(xn-[alpha]nAJxn), n[greater-or-equal, slanted]1, where J is the normalized duality mapping from E into E* and {[lambda]n} and {[theta]n} are real sequences in (0,1) satisfying certain conditions. Then it is proved that, under some mild conditions, {xn} converges strongly to x*[set membership, variant]E where Jx*[set membership, variant]A-1(0). Finally, we apply our convergence theorems to the convex minimization problems.
Approximative compactness and continuity of metric projector in Banach spaces and applications
CHEN ShuTao; HUDZIK Henryk; KOWALEWSKI Wojciech; WANG YuWen; WlSLA Marek
2008-01-01
First we prove that the approximative compactness of a nonempty set C in a normed linear space can be reformulated equivalently in another way. It is known that if C is a semi-Chebyshev closed and approximately compact set in a Banach space X, then the metric projector πC from X onto C is continuous. Under the assumption that X is midpoint locally uniformly rotund, we prove that the approximative compactness of C is also necessary for the continuity of the projector πC by the method of geometry of Banach spaces. Using this general result we find some necessary and sufficient conditions for T to have a continuous Moore-Penrose metric generalized inverse T+, where T is a bounded linear operator from an approximative compact and a rotund Banach space X into a midpoint locally uniformly rotund Banach space Y.
On Property () in Banach Lattices, Calderón–Lozanowskiĭ and Orlicz–Lorentz Spaces
Paweł Kolwicz
2001-08-01
The geometry of Calderón–Lozanowskiĭ spaces, which are strongly connected with the interpolation theory, was essentially developing during the last few years (see [4, 9, 10, 12, 13, 17]). On the other hand many authors investigated property () in Banach spaces (see [7, 19, 20, 21, 25, 26]). The first aim of this paper is to study property () in Banach function lattices. Namely a criterion for property () in Banach function lattice is presented. In particular we get that in Banach function lattice property () implies uniform monotonicity. Moreover, property () in generalized Calderón–Lozanowskiĭ function spaces is studied. Finally, it is shown that in Orlicz–Lorentz function spaces property () and uniform convexity coincide.
An Iterative Scheme for the System of Generalized Variational Inequalities in Banach Spaces
Ying LIU
2011-01-01
In this paper,we propose an iterative method of approximating solutions for a class of the system of generalized variational inequalities and give a convergence result for the iterative method in uniformly convex and uniformly smooth Banach spaces.
Ishikawa iteration process with errors for nonexpansive mappings in uniformly convex Banach spaces
Deng Lei; Li Shenghong
2000-01-01
We shall consider the behaviour of Ishikawa iteration with errors in a uniformly convex Banach space. Then we generalize the two theorems of Tan and Xu without the restrictions that C is bounded and limsupnsn
Solutions to Fractional Differential Equations with Nonlocal Initial Condition in Banach Spaces
Liang Jin
2010-01-01
Full Text Available A new existence and uniqueness theorem is given for solutions to differential equations involving the Caputo fractional derivative with nonlocal initial condition in Banach spaces. An application is also given.
Approximating zero points of accretive operators with compact domains in general Banach spaces
Miyake Hiromichi
2005-01-01
Full Text Available We prove strong convergence theorems of Mann's type and Halpern's type for resolvents of accretive operators with compact domains and apply these results to find fixed points of nonexpansive mappings in Banach spaces.
DOUBLE Φ-INEQUALITIES FOR BANACH-SPACE-VALUED MARTINGALES
Wang Yingzhan; Zhang Chao; Hou Youliang
2012-01-01
Let B be a Banach space,Φ1,Φ2 be two generalized convex Φ-functions and Ψ1,Ψ2 the Young complementary functions of Φl,Φ2 respectively with ∫tt0 ψ2(s)/sds≤c0ψ1(c0t) (t＞t0)for some constants c0 ＞ 0 and t0 ＞ 0,where ψ1 and ψ2 are the left-continuous derivative functions of Ψ 1 and Ψ2,respectively.We claim that:(i) If B is isomorphic to a p-uniformly smooth space (or q-uniformly convex space,respectively),then there exists a constant c ＞ 0 such that for any B-valued martingale f =(fn)n≥0,‖f*‖Φ1 ≤ c‖S(p)(f)‖Φ2 (or ‖S(q) (f)‖Φ1 ≤ c‖f* ‖Φ2,respectively),where f* and S(p)(f) are the maximal function and the p-variation function of f respectively; (ii) If B is a UMD space,Tvf is the martingale transform of f with respect to v =(vn)n≥0 (v* ≤ 1),then ‖(Tvf)*‖Φl ≤ c‖f*‖Φ2.
Restrictive metric regularity and generalized differential calculus in Banach spaces
Bingwu Wang
2004-10-01
Full Text Available We consider nonlinear mappings f:XÃ¢Â†Â’Y between Banach spaces and study the notion of restrictive metric regularity of f around some point xÃ‚Â¯, that is, metric regularity of f from X into the metric space E=f(X. Some sufficient as well as necessary and sufficient conditions for restrictive metric regularity are obtained, which particularly include an extension of the classical Lyusternik-Graves theorem in the case when f is strictly differentiable at xÃ‚Â¯ but its strict derivative Ã¢ÂˆÂ‡f(xÃ‚Â¯ is not surjective. We develop applications of the results obtained and some other techniques in variational analysis to generalized differential calculus involving normal cones to nonsmooth and nonconvex sets, coderivatives of set-valued mappings, as well as first-order and second-order subdifferentials of extended real-valued functions.
ON THE EXISTENCE OF COMMON FIXED POINTS FOR A PAIR OF LIPSCHITZIAN MAPPINGS IN BANACH SPACES
曾六川
2003-01-01
The existence of common fixed points for a pair of Lipschitzian mappings in Banach spaces is proved. By using this result, some common fixed point theorems are also established for these mappings in Hilbert spaces, in Lp spaces, in Hardy spaces Hp , and in Sobolev spaces Hr,p, for 1 ＜ p ＜ + ∞ and r ≥ 0.
Schuster, Thomas; Hofmann, Bernd; Kaltenbacher, Barbara
2012-10-01
Inverse problems can usually be modelled as operator equations in infinite-dimensional spaces with a forward operator acting between Hilbert or Banach spaces—a formulation which quite often also serves as the basis for defining and analyzing solution methods. The additional amount of structure and geometric interpretability provided by the concept of an inner product has rendered these methods amenable to a convergence analysis, a fact which has led to a rigorous and comprehensive study of regularization methods in Hilbert spaces over the last three decades. However, for numerous problems such as x-ray diffractometry, certain inverse scattering problems and a number of parameter identification problems in PDEs, the reasons for using a Hilbert space setting seem to be based on conventions rather than an appropriate and realistic model choice, so often a Banach space setting would be closer to reality. Furthermore, non-Hilbertian regularization and data fidelity terms incorporating a priori information on solution and noise, such as general Lp-norms, TV-type norms, or the Kullback-Leibler divergence, have recently become very popular. These facts have motivated intensive investigations on regularization methods in Banach spaces, a topic which has emerged as a highly active research field within the area of inverse problems. Meanwhile some of the most well-known regularization approaches, such as Tikhonov-type methods requiring the solution of extremal problems, and iterative ones like the Landweber method, the Gauss-Newton method, as well as the approximate inverse method, have been investigated for linear and nonlinear operator equations in Banach spaces. Convergence with rates has been proven and conditions on the solution smoothness and on the structure of nonlinearity have been formulated. Still, beyond the existing results a large number of challenging open questions have arisen, due to the more involved handling of general Banach spaces and the larger variety
WANG XIONG-RUI; Ji You-qing
2011-01-01
In this paper,the iteration xn+1 =any + (1 - αn)Tk(n)i(n)xn for a family of asymptotically nonexpansive mappings T1,T2,...,TN is originally introduced in an uniformly convex Banach space.Motivated by recent papers,we prove that under suitable conditions the iteration scheme converges strongly to the nearest common fixed point of the family of asymptotically nonexpansive mappings.The results presented in this paper expand and improve correponding ones from Hilbert spaces to uniformly convex Banach spaces,or from nonexpansive mappings to asymptotically nonexpansive mappings.
Fixed point variational solutions for uniformly continuous pseudocontractions in Banach spaces
Aniefiok Udomene
2006-03-01
Full Text Available Let E be a reflexive Banach space with a uniformly GÃƒÂ¢teaux differentiable norm, let K be a nonempty closed convex subset of E, and let T:KÃ¢Â†Â’K be a uniformly continuous pseudocontraction. If f:KÃ¢Â†Â’K is any contraction map on K and if every nonempty closed convex and bounded subset of K has the fixed point property for nonexpansive self-mappings, then it is shown, under appropriate conditions on the sequences of real numbers {ÃŽÂ±n}, {ÃŽÂ¼n}, that the iteration process z1Ã¢ÂˆÂˆK, zn+1=ÃŽÂ¼n(ÃŽÂ±nTzn+(1Ã¢ÂˆÂ’ÃŽÂ±nzn+(1Ã¢ÂˆÂ’ÃŽÂ¼nf(zn, nÃ¢ÂˆÂˆÃ¢Â„Â•, strongly converges to the fixed point of T, which is the unique solution of some variational inequality, provided that K is bounded.
Thianwan, Sornsak
2009-02-01
In this paper, we introduce a new two-step iterative scheme for two asymptotically nonexpansive nonself-mappings in a uniformly convex Banach space. Weak and strong convergence theorems are established for the new two-step iterative scheme in a uniformly convex Banach space.
Murat Ozdemir
2010-01-01
Full Text Available We introduce a new two-step iterative scheme for two asymptotically nonexpansive nonself-mappings in a uniformly convex Banach space. Weak and strong convergence theorems are established for this iterative scheme in a uniformly convex Banach space. The results presented extend and improve the corresponding results of Chidume et al. (2003, Wang (2006, Shahzad (2005, and Thianwan (2008.
STRONG CONVERGENCE OF APPROXIMATED SEQUENCES FOR NONEXPANSIVE MAPPINGS IN BANACH SPACES
无
2007-01-01
This paper studies the convergence of the sequence defined by x0∈C,xn+1=αnu+(1-αn)Txn,n=0,1,2,…, where 0 ≤αn ≤ 1, limn→∞αn = 0, ∑∞n=0 αn = ∞, and T is a nonexpansive mapping from a nonempty closed convex subset C of a Banach space X into itself. The iterative sequence {xn} converges strongly to a fixed point of T in the case when X is a uniformly convex Banach space with a uniformly Gateaux differentiable norm or a uniformly smooth Banach space only. The results presented in this paper extend and improve some recent results.
Fixed Points of α-Admissible Mappings in Cone Metric Spaces with Banach Algebra
S.K. Malhotra
2015-11-01
Full Text Available In this paper, we introduce the $\\alpha$-admissible mappings in the setting of cone metric spaces equipped with Banach algebra and solid cones. Our results generalize and extend several known results of metric and cone metric spaces. An example is presented which illustrates and shows the significance of results proved herein.
Periodic and almost periodic solutions for multi-valued differential equations in Banach spaces
E. Hanebaly
2000-03-01
Full Text Available It is known that for $omega$-periodic differential equations of monotonous type, in uniformly convex Banach spaces, the existence of a bounded solution on ${Bbb R}^+$ is equivalent to the existence of an omega-periodic solution (see Haraux [5] and Hanebaly [7, 10]. It is also known that if the Banach space is strictly convex and the equation is almost periodic and of monotonous type, then the existence of a continuous solution with a precompact range is equivalent to the existence of an almost periodic solution (see Hanebaly [8]. In this note we want to generalize the results above for multi-valued differential equations.
On well posedness of best simultaneous approximation problems in Banach spaces
无
2001-01-01
The well posedness of best simultaneous approximation problems is considered. We establish the generic results on the well posedness of the best simultaneous approximation problems for any closed weakly compact nonempty subset in a strictly convex Kadec Banach space. Further, we prove that the set of all points in E(G) such that the best simultaneous approximation problems are not well posed is a σ-porous set in E(G) when X is a uniformly convex Banach space. In addition, we also investigate the generic property of the ambiguous loci of the best simultaneous approximation.
Xie Ping DING
2012-01-01
Some classes of mixed equilibrium problems and bilevel mixed equilibrium problems are introduced and studied in reflexive Banach spaces.First,by using a minimax inequality,some new existence results of solutious and the behavior of solution set for the mixed equilibrium problems and the bilevel mixed equilibrium problems are proved under suitable assumptions without the coercive conditions.Next,by using auxiliary principle technique,some new iterative algorithms for solving the mixed equilibrium problems and the bilevel mixed equilibrium problems are suggested and analyzed.The strong convergence of the iterative sequences generated by the proposed algorithms is proved under suitable assumptions without the coercive conditions.These results are new and generalize some recent results in this field.
ISAC G.; LI Jin-lu
2005-01-01
The notion of"exceptional family of elements (EFE)" plays a very important role in solving complementarity problems. It has been applied in finite dimensional spaces and Hilbert spaces by many authors. In this paper, by using the generalized projection defined by Alber, we extend this notion from Hilbert spaces to uniformly smooth and uniformly convex Banach spaces,and apply this extension to the study of nonlinear complementarity problems in Banach spaces.
Existence and Algorithm for Solving the System of Mixed Variational Inequalities in Banach Spaces
Siwaporn Saewan
2012-01-01
Full Text Available The purpose of this paper is to study the existence and convergence analysis of the solutions of the system of mixed variational inequalities in Banach spaces by using the generalized f projection operator. The results presented in this paper improve and extend important recent results of Zhang et al. (2011 and Wu and Huang (2007 and some recent results.
Controllability of impulsive functional differential systems with infinite delay in Banach spaces
Chang Yongkui [Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070 (China)]. E-mail: lzchangyk@163.com
2007-08-15
The paper establishes a sufficient condition for the controllability of the first-order impulsive functional differential systems with infinite delay in Banach spaces. We use Schauder's fixed point theorem combined with a strongly continuous operator semigroup. An example is given to illustrate our results.
Vinod Kumar Sahu
2016-12-01
Full Text Available In this article, we consider an implicit iterative scheme for two asymptotically quasi-I-nonexpansive mappings T1, T2 and two asymptotically quasi-nonexpansive mapping I1, I2 in Banach spaces. We prove weak and strong convergence results for considered iteration to common fixed point of such mappings. Our main results improve and compliment some known results.
N-th order impulsive integro-differential equations in Banach spaces
Manfeng Hu
2004-03-01
Full Text Available We investigate the maximal and minimal solutions of initial value problem for N-th order nonlinear impulsive integro-differential equation in Banach space by establishing a comparison result and using the upper and lower solutions methods.
Bound and periodic solutions of the Riccati equation in Banach space
A. Ya. Dorogovtsev
1995-01-01
Full Text Available An abstract, nonlinear, differential equation in Banach space is considered. Conditions are presented for the existence of bounded solutions of this equation with a bounded right side, and also for the existence of stationary (periodic solutions of this equation with a stationary (periodic process in the right side.
Some G-M-type Banach spaces and K-groups of operator algebras on them
ZHONG Huaijie; CHEN Dongxiao; CHEN Jianlan
2004-01-01
By providing several new varieties of G-M-type Banachspaces according to decomposable and compoundable properties, this paper discusses the operator structures of thesespaces and the K-theory of the algebra of the operators on these G-M-type Banach spaces throughcalculation of the K-groups of the operator ideals contained in the class of Riesz operators.
Non-expansive Mappings and Iterative Methods in Uniformly Convex Banach Spaces
Hai Yun ZHOU
2004-01-01
In this article, we will investigate the properties of iterative sequence for non-expansive mappings and present several strong and weak convergence results of successive approximations to fixed points of non-expansive mappings in uniformly convex Banach spaces. The results presented in this article generalize and improve various ones concerned with constructive techniques for the fixed points of non-expansive mappings.
On the periodic mild solutions to complete higher order differential equations on Banach spaces
Lan Nguyen
2011-08-01
Full Text Available For the complete higher order differential equation u(n(t=∑k=0n-1Aku(k(t+f(t, 0 ≤ t ≤ T, on a Banach space E, we give necessary and sufficient conditions for the periodicity of mild solutions. The results, which are proved in a simple manner, generalize some well-known ones.
Wan-sheng WANG; Shou-fu LI; Run-sheng YANG
2012-01-01
A series of contractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations (NFDEs) in Banach spaces are obtained,which provide unified theoretical foundation for the contractivity analysis of solutions to nonlinear problems in functional differential equations (FDEs),neutral delay differential equations (NDDEs) and NFDEs of other types which appear in practice.
Strong convergence theorems for nonexpansive semi-groups in Banach spaces
无
2007-01-01
Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the corresponding results of ShiojiTakahashi, Suzuki, Xu and Aleyner-Reich, but also give a partially affirmative answer to the open questions raised by Suzuki and Xu.
Chang, Y.-K. [Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070 (China)], E-mail: lzchangyk@163.com; Anguraj, A. [Department of Mathematics, PSG College of Arts and Science, Coimbatore 641 014, Tamil Nadu (India)], E-mail: angurajpsg@yahoo.com; Mallika Arjunan, M. [Department of Mathematics, PSG College of Arts and Science, Coimbatore 641 014, Tamil Nadu (India)], E-mail: arjunphd07@yahoo.co.in
2009-02-28
In this work, we establish a sufficient condition for the controllability of the first-order impulsive neutral functional differential inclusions with infinite delay in Banach spaces. The results are obtained by using the Dhage's fixed point theorem.
K. Balachandran
2006-09-01
Full Text Available In this paper we prove the existence of mild and strong solutions of nonlinear time varying delay integrodifferential equations of Sobolev type with nonlocal conditions in Banach spaces. The results are obtained by using the theory of compact semigroups and Schaefer's fixed point theorem.
Approximation Methods for Common Fixed Points of Mean Nonexpansive Mapping in Banach Spaces
Zhaohui Gu
2008-02-01
Full Text Available Let X be a uniformly convex Banach space, and let S,Ã‚Â T be a pair of mean nonexpansive mappings. In this paper, it is proved that the sequence of Ishikawa iterations associated with S and T converges to the common fixed point of S and T.
Weak and strong convergence theorems for nonexpansive semigroups in Banach spaces
Takahashi Wataru
2005-01-01
Full Text Available We introduce an implicit iterative process for a nonexpansive semigroup and then we prove a weak convergence theorem for the nonexpansive semigroup in a uniformly convex Banach space which satisfies Opial's condition. Further, we discuss the strong convergence of the implicit iterative process.
Xing-hui GAO; Hai-yun ZHOU
2012-01-01
In this paper,we consider hybrid algorithms for finding common elements of the set of common fixed points of two families quasi-φ-non-expansive mappings and the set of solutions of an equilibrium problem.We establish strong convergence theorems of common elements in uniformly smooth and strictly convex Banach spaces with the property (K).
A RANDOM FIXED POINT ITERATION FOR THREE RANDOM OPERATORS ON UNIFORMLY CONVEX BANACH SPACES
Binayak S. Choudhury
2003-01-01
In the present paper we introduce a random iteration scheme for three random operators defined on a closed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixed point of three random operators. The result is also an extension of a known theorem in the corresponding non-random case.
曾六川
2003-01-01
A new class of almost asymptotically nonexpansive type mappings in Banach spaces is introduced, which includes a number of known classes of nonlinear Lipschitzian mappings and non-Lipschitzian mappings in Banach spaces as special cases; for example,the known classes of nonexpansive mappings, asymptotically nonexpansive mappings and asymptotically nonexpansive type mappings. The convergence problem of modified Ishikawa iterative sequences with errors for approximating fixed points of almost asymptotically nonexpansive type mappings is considered. Not only S. S. Chang' s inequality but also H.K. Xu' s one for the norms of Banach spaces are applied to make the error estimate between the exact fixed point and the approximate one. Moreover, Zhang Shi-sheng ' s method (Applied Mathematics and Mechanics ( English Edition ), 2001,22 (1) :25 - 34) for making the convergence analysis of modified Ishikawa iterative sequences with errors is extended to the case of almost asymptotically nonexpansive type mappings. The new convergence criteria of modified Ishikawa iterative sequences with errors for finding fixed points of almost asymptotically nonexpansive type mappings in uniformly convex Banach spaces are presented. Also, the new convergence criteria of modified Mann iterative sequences with errors for this class of mappings are immediately obtained from these criteria. The above results unify, improve and generalize Zhang Shi-sheng's ones on approximating fixed points of asymptotically nonexpansive type mappings by the modified Ishikawa and Mann iterative sequences with errors.
Weak and strong convergence theorems for nonexpansive semigroups in Banach spaces
Wataru Takahashi
2005-10-01
Full Text Available We introduce an implicit iterative process for a nonexpansive semigroup and then we prove a weak convergence theorem for the nonexpansive semigroup in a uniformly convex Banach space which satisfies Opial's condition. Further, we discuss the strong convergence of the implicit iterative process.
On the fixed points of nonexpansive mappings in direct sums of Banach spaces
Wiśnicki, Andrzej
2011-01-01
We show that if a Banach space X has the weak fixed point property for nonexpansive mappings and Y has the generalized Gossez-Lami Dozo property or is uniformly convex in every direction, then the direct sum of X and Y with a strictly monotone norm has the weak fixed point property. The result is new even if Y is finite-dimensional.
Dehghan, Hossein
2011-01-01
In this paper, a strong convergence theorem for asymptotically nonexpansive mappings in a uniformly convex and smooth Banach space is proved by using metric projections. This theorem extends and improves the recent strong convergence theorem due to Matsushita and Takahashi [ Appl. Math. Comput. 196 (2008) 422-425] which was established for nonexpansive mappings.
Mann Type Implicit Iteration Approximation for Multivalued Mappings in Banach Spaces
Chen Rudong
2010-01-01
Full Text Available Let be a nonempty compact convex subset of a uniformly convex Banach space and let be a multivalued nonexpansive mapping. For the implicit iterates , , , . We proved that converges strongly to a fixed point of under some suitable conditions. Our results extended corresponding ones and revised a gap in the work of Panyanak (2007.
Yan Hao, Xiaoshuang Wang, Aihua Tong
2012-11-01
Full Text Available In this paper, an implicit iterative process with mixed errors for two finite family of asymptotically nonexpansive mappings is considered. Weak and strong convergence theorems for common fixed points of two finite family of asymptotically nonexpansive mappings are established in a uniformly convex Banach space.
Approximation Methods for Common Fixed Points of Mean Nonexpansive Mapping in Banach Spaces
Li Yongjin
2008-01-01
Full Text Available Let be a uniformly convex Banach space, and let be a pair of mean nonexpansive mappings. In this paper, it is proved that the sequence of Ishikawa iterations associated with and converges to the common fixed point of and .
Terminal value problems of impulsive integro-differential equations in Banach spaces
Dajun Guo
1997-01-01
Full Text Available This paper uses cone theory and the monotone iterative technique to investigate the existence of minimal nonnegative solutions of terminal value problems for first order nonlinear impulsive integro-differential equations of mixed type in a Banach space.
On the correct formulation of a nonlinear differential equations in Banach space
Mahmoud M. El-Borai
2001-01-01
Full Text Available We study, the existence and uniqueness of the initial value problems in a Banach space E for the abstract nonlinear differential equation (dn−1/dtn−1(du/dt+Au=B(tu+f(t,W(t, and consider the correct solution of this problem. We also give an application of the theory of partial differential equations.
Hongxia Fan
2011-01-01
Full Text Available By means of the fixed point theory of strict set contraction operators, we establish a new existence theorem on multiple positive solutions to a singular boundary value problem for second-order impulsive differential equations with periodic boundary conditions in a Banach space. Moreover, an application is given to illustrate the main result.
EIGENVECTORS OF SYSTEM OF HAMMERSTEININTEGRAL EQUATIONS IN BANACH SPACES AND APPLICATIONS
无
2000-01-01
In this paper,the author investigates the existence of eigenvectors of system of Hammerstein integral equations in Banach spaces by means of fixed point index theory.He also gives some applications to a system of Sturm-Liouville problems of ordinary differential equations.
NONLOCAL INITIAL PROBLEM FOR NONLINEAR NONAUTONOMOUS DIFFERENTIAL EQUATIONS IN A BANACH SPACE
M.I.Gil＇
2004-01-01
The nonlocal initial problem for nonlinear nonautonomous evolution equations in a Banach space is considered. It is assumed that the nonlinearities have the local Lipschitz properties. The existence and uniqueness of mild solutions are proved. Applications to integro-differential equations are discussed. The main tool in the paper is the normalizing mapping (the generalized norm).
Gu Feng
2006-01-01
Full Text Available The purpose of this paper is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of Chang and Cho (2003, Xu and Ori (2001, and Zhou and Chang (2002.
POSITIVE SOLUTIONS TO SEMI-LINEAR SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACE
无
2008-01-01
In this paper,we study the existence of positive periodic solution to some second- order semi-linear differential equation in Banach space.By the fixed point index theory, we prove that the semi-linear differential equation has two positive periodic solutions.
Approximate Fixed Point Theorems in Banach Spaces with Applications in Game Theory
Brânzei, R.; Morgan, J.; Scalzo, V.; Tijs, S.H.
2002-01-01
In this paper some new approximate fixed point theorems for multifunctions in Banach spaces are presented and a method is developed indicating how to use approximate fixed point theorems in proving the existence of approximate Nash equilibria for non-cooperative games.
The Equivalence of Ishikawa-Mann and Multistep Iterations in Banach Space
Liping Yang
2007-01-01
Let E be a real Banach space and T be a continuous Φ-strongly accretive operator. By using a new analytical method,it is proved that the convergence of Mann,Ishikawa and three-step iterations are equivalent to the convergence of multistep iteration.The results of this paper extend the results of Rhoades and Soltuz in some aspects.
Xue-song Li
2009-01-01
Full Text Available We study the strong convergence of two kinds of viscosity iteration processes for approximating common fixed points of the pseudocontractive semigroup in uniformly convex Banach spaces with uniformly Gâteaux differential norms. As special cases, we get the strong convergence of the implicit viscosity iteration process for approximating common fixed points of the nonexpansive semigroup in Banach spaces satisfying some conditions. The results presented in this paper extend and generalize some results concerned with the nonexpansive semigroup in (Chen and He, 2007 and the pseudocontractive mapping in (Zegeye et al., 2007 to the pseudocontractive semigroup in Banach spaces under different conditions.
ASYMPTOTICALLY ISOMETRIC COPIES OF lp (1≤p＜∞) AND c0 IN BANACH SPACES
Chen Dongyang
2006-01-01
Let X be a Banach space. If there exists a quotient space of X which is asymptotically isometric to l1, then X contains complemented asymptotically isometric copies of l1. Every infinite dimensional closed subspace of l1 contains a complemented subspace of l1 which is asymptotically isometric to l1. Let X be a separable Banach space such that X* contains asymptotically isometric copies of lp (1 ＜ p ＜∞). Then there exists a quotient space of X which is asymptotically isometric to lq (1/p+1/q=1). Complementedasymptotically isometric copies of c0 in K(X, Y) and W(X, Y) are discussed. Let X be a Gelfand-Phillips space. If X contains asymptotically isometric copies of c0, it has to contain complemented asymptotically isometric copies of c0.
詹华英
2008-01-01
The definition of property A with constant a was introduced by D. M. Speegle, who proved that every infinite dimensional separable uniformly smooth Banach space has property A with constant α∈ [0, 1). In this paper, we give a sufficient condition for a Banach space to have property A with constant α∈ [0, 1), and some remarks on Speegle's paper [1].
Boulbeba Abdelmoumen; Aref Jeribi; Maher Mnif
2012-01-01
In this paper,we define new measures called respectively graph measure of noncompactness and graph measure of weak noncompactness.Moreover,we apply the obtained results to discuss the incidence of some perturbation results realized in [2] on the behavior of essential spectra of such closed densely defined linear operators on Banach spaces.These results are exploited to investigate the essential spectra of a multidimensional neutron transport operator on L1 spaces.
On Landweber-Kaczmarz methods for regularizing systems of ill-posed equations in Banach spaces
Leitão, A.; Marques Alves, M.
2012-10-01
In this paper, iterative regularization methods of Landweber-Kaczmarz type are considered for solving systems of ill-posed equations modeled (finitely many) by operators acting between Banach spaces. Using assumptions of uniform convexity and smoothness on the parameter space, we are able to prove a monotony result for the proposed method, as well as to establish convergence (for exact data) and stability results (in the noisy data case).
Qinghai He
2013-01-01
Full Text Available In general Banach spaces, we consider a vector optimization problem (SVOP in which the objective is a set-valued mapping whose graph is the union of finitely many polyhedra or the union of finitely many generalized polyhedra. Dropping the compactness assumption, we establish some results on structure of the weak Pareto solution set, Pareto solution set, weak Pareto optimal value set, and Pareto optimal value set of (SVOP and on connectedness of Pareto solution set and Pareto optimal value set of (SVOP. In particular, we improved and generalize, Arrow, Barankin, and Blackwell’s classical results in Euclidean spaces and Zheng and Yang’s results in general Banach spaces.
Existence Results for Differential Inclusions with Nonlinear Growth Conditions in Banach Spaces
Messaoud Bounkhel
2013-01-01
Full Text Available In the Banach space setting, the existence of viable solutions for differential inclusions with nonlinear growth; that is, ẋ(t∈F(t,x(t a.e. on I, x(t∈S, ∀t∈I, x(0=x0∈S, (*, where S is a closed subset in a Banach space , I=[0,T], (T>0, F:I×S→, is an upper semicontinuous set-valued mapping with convex values satisfying F(t,x⊂c(tx+xp, ∀(t,x∈I×S, where p∈ℝ, with p≠1, and c∈C([0,T],ℝ+. The existence of solutions for nonconvex sweeping processes with perturbations with nonlinear growth is also proved in separable Hilbert spaces.
Cauchy-Rassias Stability of Cauchy-Jensen Additive Mappings in Banach Spaces
Choonkil BAAK
2006-01-01
Let X, Y be vector spaces. It is shown that if a mapping f: X → Y satisfiesf(x+y/2+z)+f(x-y/2+z)=f(x)+2f(z), (0.1)f(x+y/2+z)-f(x-y/2+z)= f(y), (0.2)or2f(x+y/2+z)=f(x)+f(y)+2f(z) (0.3)for all x, y, z ∈ X, then the mapping f: X → Y is Cauchy additive.Furthermore, we prove the Cauchy-Rassias stability of the functional equations (0.1), (0.2) and (0.3) in Banach spaces. The results are applied to investigate isomorphisms between unital Banach algebra.
ON THE EXISTENCE OF FIXED POINTS FOR LIPSCHITZIAN SEMIGROUPS IN BANACH SPACES
无
2001-01-01
Let C be a nonempty bounded subset of a p-uniformly convex Banach space X, and T ={T(t):t∈S}be a Lipschitzian semigroup on C with lim inf|||T(t)||| ＜ Np, where Np isn→∞t∈s the normal structure coefficient of X. Suppose also there exists a nonempty bounded closed convex subset E of C with the following properties: (P1)x ∈ E implies ωw(x) E; (P2)T is asymptotically regular on E. The authors prove that there exists a z ∈ E such that T(s)z = z for all s ∈ S. Further, under the similar condition, the existence of fixed points of Lipschitzian semigroups in a uniformly convex Banach space is discussed.
The Arc Distortion in QH Inner Ψ-uniform (or Convex) Domains in Real Banach Spaces
Man Zi HUANG; Xian Tao WANG
2011-01-01
Let D and D' be domains in real Banach spaces of dimension at least 2.The main aim of this paper is to study certain arc distortion properties in the quasihyperbolic metric defined in real Banach spaces.In particular,when D' is a QH inner Ψ-uniform domain with Ψ being a slow (or a convex domain),we investigate the following:For positive constants c,h,C,M,suppose a homeomorphism f:D → D' takes each of the 10-neargeodesics in D to (c,h)-solid in D'.Then f is C-coarsely MLipschitz in the quasihyperbolic metric.These are generalizations of the corresponding result obtained recently by V(a)is(a)l(a).
Landweber-Kaczmarz method in Banach spaces with inexact inner solvers
Jin, Qinian
2016-10-01
In recent years the Landweber-Kaczmarz method has been proposed for solving nonlinear ill-posed inverse problems in Banach spaces using general convex penalty functions. The implementation of this method involves solving a (nonsmooth) convex minimization problem at each iteration step and the existing theory requires its exact resolution which in general is impossible in practical applications. In this paper we propose a version of the Landweber-Kaczmarz method in Banach spaces in which the minimization problem involved in each iteration step is solved inexactly. Based on the \\varepsilon -subdifferential calculus we give a convergence analysis of our method. Furthermore, using Nesterov's strategy, we propose a possible accelerated version of the Landweber-Kaczmarz method. Numerical results on computed tomography and parameter identification in partial differential equations are provided to support our theoretical results and to demonstrate our accelerated method.
LI Shoufu
2005-01-01
A series of stability, contractivity and asymptotic stability results of the solutions to nonlinear stiff Volterra functional differential equations (VFDEs) in Banach spaces is obtained, which provides the unified theoretical foundation for the stability analysis of solutions to nonlinear stiff problems in ordinary differential equations(ODEs), delay differential equations(DDEs), integro-differential equations(IDEs) and VFDEs of other type which appear in practice.
Haiqing Wang
2012-01-01
Full Text Available Let be a uniformly convex Banach space and ={(∶0≤0((≠∅. Consider the iterative method that generates the sequence {} by the algorithm +1=(++(1−−(1/∫0(,≥0, where {}, {}, and {} are three sequences satisfying certain conditions, ∶→ is a contraction mapping. Strong convergence of the algorithm {} is proved assuming either has a weakly continuous duality map or has a uniformly Gâteaux differentiable norm.
Uniform exponential stability of linear periodic systems in a Banach space
David N. Cheban
2001-01-01
Full Text Available This article is devoted to the study of linear periodic dynamical systems, possessing the property of uniform exponential stability. It is proved that if the Cauchy operator of these systems possesses a certain compactness property, then the asymptotic stability implies the uniform exponential stability. We also show applications to different classes of linear evolution equations, such as ordinary linear differential equations in the space of Banach, retarded and neutral functional differential equations, some classes of evolution partial differential equations.
On some Banach space constants arising in nonlinear fixed point and eigenvalue theory
Erzakova Nina A
2004-01-01
Full Text Available As is well known, in any infinite-dimensional Banach space one may find fixed point free self-maps of the unit ball, retractions of the unit ball onto its boundary, contractions of the unit sphere, and nonzero maps without positive eigenvalues and normalized eigenvectors. In this paper, we give upper and lower estimates, or even explicit formulas, for the minimal Lipschitz constant and measure of noncompactness of such maps.
On some Banach space constants arising in nonlinear fixed point and eigenvalue theory
Martin Väth
2004-12-01
Full Text Available As is well known, in any infinite-dimensional Banach space one may find fixed point free self-maps of the unit ball, retractions of the unit ball onto its boundary, contractions of the unit sphere, and nonzero maps without positive eigenvalues and normalized eigenvectors. In this paper, we give upper and lower estimates, or even explicit formulas, for the minimal Lipschitz constant and measure of noncompactness of such maps.
MIXED MONOTONE ITERATIVE TECHNIQUES FOR SEMILINEAR EVOLUTION EQUATIONS IN BANACH SPACES
王良龙; 王志成
2004-01-01
This paper is concerned with initial value problems for semilinear evolution equations in Banach spaces. The abstract iterative schemes are constructed by combining the theory of semigroups of linear operators and the method of mixed monotone iterations. Some existence results on minimal and maximal (quasi)solutions are established for abstract semilinear evolution equations with mixed monotone or mixed quasimonotone nonlinear terms. To illustrate the main results, applications to ordinary differential equations and partial differential equations are also given.
ON A FAMILY OF CHEBYSHEV-HALLEY TYPE METHODS IN BANACH SPACE UNDER WEAKER SMALE CONDITION
无
2000-01-01
In this paper, we discuss local convergence of a family of Chebychev-Halley type methods with a parameter θ∈[0,1] in Banach space using Smale-type δ criterion under 2-th γ-condition. We will see that the properties of the condition used for local convergence is much more different from that used in [6][15] for the semi-local convergence.
On a New Geometric Constant Related to the Modulus of Smoothness of a Banach Space
Yasuji TAKAHASHI; Mikio KATO
2014-01-01
We shall introduce a new geometric constant A(X) of a Banach space X, which is closely related to the modulus of smoothnessρX(τ), and investigate it in relation with the constant A2(X) by Baronti et al., the von Neumann-Jordan constant CN J (X ) and the James constant J (X ). A sequence of recent results on these constants as well as some other geometric constants will be strengthened and improved.
CHEN Fang-qi; TIAN Rui-lan; CHEN Yu-shu
2006-01-01
Under loose conditions, the existence of solutions to initial value problem are studied for second order impulsive integro-differential equation with infinite moments of impulse effect on the positive half real axis in Banach spaces. By the use of recurrence method, Tonelii sequence and the locally convex topology, the new existence theorems are achieved, which improve the related results obtained by Guo Da-jun.
Yun-zhi Zou
2012-01-01
Full Text Available A new class of generalized dynamical systems involving generalized f-projection operators is introduced and studied in Banach spaces. By using the fixed-point theorem due to Nadler, the equilibrium points set of this class of generalized global dynamical systems is proved to be nonempty and closed under some suitable conditions. Moreover, the solutions set of the systems with set-valued perturbation is showed to be continuous with respect to the initial value.
Messaoud Bounkhel
2015-01-01
Full Text Available The present paper is devoted to the study of the generalized projection πK:X∗→K, where X is a uniformly convex and uniformly smooth Banach space and K is a nonempty closed (not necessarily convex set in X. Our main result is the density of the points x∗∈X∗ having unique generalized projection over nonempty close sets in X. Some minimisation principles are also established. An application to variational problems with nonconvex sets is presented.
Messaoud Bounkhel
2015-01-01
The present paper is devoted to the study of the generalized projection πK:X∗→K, where X is a uniformly convex and uniformly smooth Banach space and K is a nonempty closed (not necessarily convex) set in X. Our main result is the density of the points x∗∈X∗ having unique generalized projection over nonempty close sets in X. Some minimisation principles are also established. An application to variational problems with nonconvex sets is presented.
Suzuki Tomonari
2006-01-01
Full Text Available We prove Browder's type strong convergence theorems for infinite families of nonexpansive mappings. One of our main results is the following: let be a bounded closed convex subset of a uniformly smooth Banach space . Let be an infinite family of commuting nonexpansive mappings on . Let and be sequences in satisfying for . Fix and define a sequence in by for . Then converges strongly to , where is the unique sunny nonexpansive retraction from onto .
Mann Type Implicit Iteration Approximation for Multivalued Mappings in Banach Spaces
Huimin He
2010-01-01
Full Text Available Let K be a nonempty compact convex subset of a uniformly convex Banach space E and let T be a multivalued nonexpansive mapping. For the implicit iterates x0∈K, xn=αnxn-1+(1-αnyn, yn∈Txn, n≥1. We proved that {xn} converges strongly to a fixed point of T under some suitable conditions. Our results extended corresponding ones and revised a gap in the work of Panyanak (2007.
Bin-Chao Deng
2014-01-01
Full Text Available This paper aims to use a hybrid algorithm for finding a common element of a fixed point problem for a finite family of asymptotically nonexpansive mappings and the set solutions of mixed equilibrium problem in uniformly smooth and uniformly convex Banach space. Then, we prove some strong convergence theorems of the proposed hybrid algorithm to a common element of the above two sets under some suitable conditions.
Convergence of implicit iterates with errors for mappings with unbounded domain in Banach spaces
Hafiz Fukhar-Ud-Din
2005-01-01
Full Text Available We prove that an implicit iterative process with errors converges weakly and strongly to a common fixed point of a finite family of asymptotically quasi-nonexpansive mappings on unbounded sets in a uniformly convex Banach space. Our results generalize and improve upon, among others, the corresponding recent results of Sun (2003 in the following two different directions: (i domain of the mappings is unbounded, (ii the iterative sequence contains an error term.
GLOBAL SOLUTIONS OF SYSTEMS OF NONLINEAR IMPULSIVE VOLTERRA INTEGRAL EQUATIONS IN BANACH SPACES
陈芳启; 陈予恕
2001-01-01
The existence of solutions for systems of nonlinear impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces is studied. Some existence theorems of extremal solutions are obtained,which extend the related results for this class of equations on a finite interval with a finite number of moments of impulse effect. The results are demonstrated by means of an example of an infinite systems for impulsive integral equations.
Hansmann, Marcel
2015-01-01
In the first part of this paper we provide a self-contained introduction to (regularized) perturbation determinants for operators in Banach spaces. In the second part, we use these determinants to derive new bounds on the discrete eigenvalues of compactly perturbed operators, broadly extending some recent results by Demuth et al. In addition, we also establish new bounds on the discrete eigenvalues of generators of $C_0$-semigroups.
Integration over an Infinite-Dimensional Banach Space and Probabilistic Applications
Claudio Asci
2014-01-01
Full Text Available We study, for some subsets I of N*, the Banach space E of bounded real sequences {xn}n∈I. For any integer k, we introduce a measure over (E,B(E that generalizes the k-dimensional Lebesgue measure; consequently, also a theory of integration is defined. The main result of our paper is a change of variables' formula for the integration.
Weak and Strong Convergence Theorems for Nonexpansive Mappings in Banach Spaces
Su Yongfu
2008-01-01
Full Text Available Abstract The purpose of this paper is to introduce two implicit iteration schemes for approximating fixed points of nonexpansive mapping and a finite family of nonexpansive mappings , respectively, in Banach spaces and to prove weak and strong convergence theorems. The results presented in this paper improve and extend the corresponding ones of H.-K. Xu and R. Ori, 2001, Z. Opial, 1967, and others.
2-一致凸Banach空间的特征不等式%A Character Inequality of the 2-Uniformly Convex Banach Space
李婷婷; 乌日娜; 苏雅拉图
2012-01-01
In this paper,the character inequality in the 2-uniformly convex Banach space is studied. By the method of Banach space theory, this problem is discussed in the 2- uniformly convex Banach space, a character inequality of the 2-uniformly convex Banach space is obtained by combining the definition of 2- uniformly convex Banach space. Moreover, a corresponding result in the locally 2-uniformly convex Banach space is established.%研究了2-一致凸Banach空间的特征不等式问题.在2-一致凸Banach空间中,利用Banach空间理论的方法,结合2-一致凸Banach空间的定义,给出了2-一致凸Banach空间X的一个特征不等式,并将此结果推广到局部2-一致凸Banach空间的情形.
On Linear Isometries of Banach Lattices in $\\mathcal{C}_0()$-Spaces
José M Isidro
2009-11-01
Consider the space $\\mathcal{C}_0()$ endowed with a Banach lattice-norm $\\|\\cdot p\\|$ that is not assumed to be the usual spectral norm $\\|\\cdot p\\|_∞$ of the supremum over . A recent extension of the classical Banach-Stone theorem establishes that each surjective linear isometry of the Banach lattice $(\\mathcal{C}_0(),\\|\\cdot p\\|)$ induces a partition of into a family of finite subsets $S\\subset$ along with a bijection $T:→$ which preserves cardinality, and a family $[u(S):S\\in]$ of surjective linear maps $u(S):\\mathcal{C}(T(S))→\\mathcal{C}(S)$ of the finite-dimensional *-algebras $\\mathcal{C}(S)$ such that $$(U f)|_{T(S)}=u(S)(f|_S) \\quad \\forall f\\in\\mathcal{C}_0() \\quad \\forall S\\in.$$ Here we endow the space of finite sets $S\\subset$ with a topology for which the bijection and the map are continuous, thus completing the analogy with the classical result.
Convergence on Composite Iterative Schemes for Nonexpansive Mappings in Banach Spaces
Jong Soo Jung
2008-05-01
Full Text Available Let E be a reflexive Banach space with a uniformly GÃƒÂ¢teaux differentiable norm. Suppose that every weakly compact convex subset of E has the fixed point property for nonexpansive mappings. Let C be a nonempty closed convex subset of E, f:CÃ¢Â€Â‰Ã¢Â€Â‰Ã¢Â†Â’Ã¢Â€Â‰Ã¢Â€Â‰C a contractive mapping (or a weakly contractive mapping, and T:CÃ¢Â€Â‰Ã¢Â€Â‰Ã¢Â†Â’Ã¢Â€Â‰Ã¢Â€Â‰C nonexpansive mapping with the fixed point set F(TÃ¢Â€Â‰Ã¢Â€Â‰Ã¢Â‰Â Ã¢Â€Â‰Ã¢Â€Â‰Ã¢ÂˆÂ…. Let {xn} be generated by a new composite iterative scheme: yn=ÃŽÂ»nf(xn+(1Ã¢ÂˆÂ’ÃŽÂ»nTxn, xn+1=(1Ã¢ÂˆÂ’ÃŽÂ²nyn+ÃŽÂ²nTyn, (nÃ¢Â‰Â¥0. It is proved that {xn} converges strongly to a point in F(T, which is a solution of certain variational inequality provided that the sequence {ÃŽÂ»n}Ã¢ÂŠÂ‚(0,1 satisfies limnÃ¢Â†Â’Ã¢ÂˆÂžÃŽÂ»n=0 and Ã¢ÂˆÂ‘n=1Ã¢ÂˆÂžÃŽÂ»n=Ã¢ÂˆÂž, {ÃŽÂ²n}Ã¢ÂŠÂ‚[0,a for some 0
On positive solutions of functional-differential equations in banach spaces
Zima Mirosława
2001-01-01
Full Text Available In this paper, we deal with two point boundary value problem (BVP for the functional-differential equation of second order where the function takes values in a cone of a Banach space . For and we obtain the BVP with reflection of the argument. Applying fixed point theorem on strict set-contraction from G. Li, Proc. Amer. Math. Soc. 97 (1986, 277–280, we prove the existence of positive solution in the space . Some inequalities involving and the respective Green's function are used. We also give the application of our existence results to the infinite system of functional–differential equations in the case .
τ-CHEBYSHEV AND τ-COCHEBYSHEV SUBPSACES OF BANACH SPACES
H. Mazaheri
2006-01-01
The concepts of quasi-Chebyshev and weakly-Chebyshev and σ-Chebyshev were defined [3 - 7], and as a counterpart to best approximation in normed linear spaces, best coapproximation was introduced by Franchetti and Furi[1]. In this research, we shall define τ-Chebyshev subspaces and τ-cochebyshev subspaces of a Banach space, in which the property τ is compact or weakly-compact, respectively. A set of necessary and sufficient theorems under which a subspace is τ-Chebyshev is defined.
Fixed Point Theorems for Suzuki Generalized Nonexpansive Multivalued Mappings in Banach Spaces
Abkar A
2010-01-01
Full Text Available In the first part of this paper, we prove the existence of common fixed points for a commuting pair consisting of a single-valued and a multivalued mapping both satisfying the Suzuki condition in a uniformly convex Banach space. In this way, we generalize the result of Dhompongsa et al. (2006. In the second part of this paper, we prove a fixed point theorem for upper semicontinuous mappings satisfying the Suzuki condition in strictly spaces; our result generalizes a recent result of Domínguez-Benavides et al. (2009.
Fixed Point Theorems for Suzuki Generalized Nonexpansive Multivalued Mappings in Banach Spaces
A. Abkar
2010-01-01
Full Text Available In the first part of this paper, we prove the existence of common fixed points for a commuting pair consisting of a single-valued and a multivalued mapping both satisfying the Suzuki condition in a uniformly convex Banach space. In this way, we generalize the result of Dhompongsa et al. (2006. In the second part of this paper, we prove a fixed point theorem for upper semicontinuous mappings satisfying the Suzuki condition in strictly L(τ spaces; our result generalizes a recent result of Domínguez-Benavides et al. (2009.
Weak Convergence Theorems for a Countable Family of Strict Pseudocontractions in Banach Spaces
Cholamjiak Prasit
2010-01-01
Full Text Available We investigate the convergence of Mann-type iterative scheme for a countable family of strict pseudocontractions in a uniformly convex Banach space with the Fréchet differentiable norm. Our results improve and extend the results obtained by Marino-Xu, Zhou, Osilike-Udomene, Zhang-Guo and the corresponding results. We also point out that the condition given by Chidume-Shahzad (2010 is not satisfied in a real Hilbert space. We show that their results still are true under a new condition.
Constructive techniques for zeros of monotone mappings in certain Banach spaces.
Diop, C; Sow, T M M; Djitte, N; Chidume, C E
2015-01-01
Let E be a 2-uniformly convex real Banach space with uniformly Gâteaux differentiable norm, and [Formula: see text] its dual space. Let [Formula: see text] be a bounded strongly monotone mapping such that [Formula: see text] For given [Formula: see text] let [Formula: see text] be generated by the algorithm: [Formula: see text]where J is the normalized duality mapping from E into [Formula: see text] and [Formula: see text] is a real sequence in (0, 1) satisfying suitable conditions. Then it is proved that [Formula: see text] converges strongly to the unique point [Formula: see text] Finally, our theorems are applied to the convex minimization problem.
Bredies, Kristian
2009-01-01
We consider the task of computing an approximate minimizer of the sum of a smooth and a non-smooth convex functional, respectively, in Banach space. Motivated by the classical forward-backward splitting method for the subgradients in Hilbert space, we propose a generalization which involves the iterative solution of simpler subproblems. Descent and convergence properties of this new algorithm are studied. Furthermore, the results are applied to the minimization of Tikhonov-functionals associated with linear inverse problems and semi-norm penalization in Banach spaces. With the help of Bregman-Taylor-distance estimates, rates of convergence for the forward-backward splitting procedure are obtained. Examples which demonstrate the applicability are given, in particular, a generalization of the iterative soft-thresholding method by Daubechies, Defrise and De Mol to Banach spaces as well as total-variation-based image restoration in higher dimensions are presented.
Lu-Chuan Ceng
2013-01-01
Full Text Available We introduce composite implicit and explicit iterative algorithms for solving a general system of variational inequalities and a common fixed point problem of an infinite family of nonexpansive mappings in a real smooth and uniformly convex Banach space. These composite iterative algorithms are based on Korpelevich's extragradient method and viscosity approximation method. We first consider and analyze a composite implicit iterative algorithm in the setting of uniformly convex and 2-uniformly smooth Banach space and then another composite explicit iterative algorithm in a uniformly convex Banach space with a uniformly Gâteaux differentiable norm. Under suitable assumptions, we derive some strong convergence theorems. The results presented in this paper improve, extend, supplement, and develop the corresponding results announced in the earlier and very recent literatures.
Lu-Chuan Ceng
2013-01-01
Full Text Available We introduce Mann-type extragradient methods for a general system of variational inequalities with solutions of a multivalued variational inclusion and common fixed points of a countable family of nonexpansive mappings in real smooth Banach spaces. Here the Mann-type extragradient methods are based on Korpelevich’s extragradient method and Mann iteration method. We first consider and analyze a Mann-type extragradient algorithm in the setting of uniformly convex and 2-uniformly smooth Banach space and then another Mann-type extragradient algorithm in a smooth and uniformly convex Banach space. Under suitable assumptions, we derive some weak and strong convergence theorems. The results presented in this paper improve, extend, supplement, and develop the corresponding results announced in the earlier and very recent literature.
A NEW CLASS OF BILEVEL GENERALIZED MIXED EQUILIBRIUM PROBLEMS IN BANACH SPACES
Ding Xieping
2012-01-01
A new class of bilevel generalized mixed equilibrium problems involving setvalued mappings is introduced and studied in a real Banach space.By using the auxiliary principle technique,new iterative algorithms for solving the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems involving set-valued mappings are suggested and analyzed.Existence of solutions and strong convergence of the iterative sequences generated by the algorithms are proved under quite mild conditions.The behavior of the solution set of the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems is also discussed.These results are new and generalize some recent results in this field.
Wen ZHANG
2012-01-01
By a ball-covering B of a Banach space X,we mean thatB is a collection of open (or closed)balls off the origin whose union contains the unit sphere of X; and X is said to have the ball-covering property provided it admits a ball-covering of countably many balls.This paper shows that universal finite representability and B-convexity of X can be characterized by properties of ball-coverings of its finite dimensioral subspaces.
C0-semigroups of linear operators on some ultrametric Banach spaces
Toka Diagana
2006-01-01
Full Text Available C0-semigroups of linear operators play a crucial role in the solvability of evolution equations in the classical context. This paper is concerned with a brief conceptualization of C0-semigroups on (ultrametric free Banach spaces E. In contrast with the classical setting, the parameter of a given C0-semigroup belongs to a clopen ball Ωr of the ground field K. As an illustration, we will discuss the solvability of some homogeneous p-adic differential equations.
A model of CT dose profiles in Banach space; with applications to CT dosimetry
Weir, Victor J.
2016-07-01
In this paper the scatter component of computed tomography dose profiles is modeled using the solution to a nonlinear ordinary differential equation. This scatter function is summed with a modeled primary function of approximate trapezoidal shape. The primary dose profile is modeled to include the analytic continuation of the Heaviside step function. A mathematical theory is developed in a Banach space. The modeled function is used to accurately fit data from a 256-slice GE Revolution scanner. A 60 cm long body phantom is assembled and used for data collection with both a pencil chamber and a Farmer-type chamber.
Existence results for a class of parabolic evolution equations in Banach spaces
WangJing; XueXingmei
2003-01-01
We discuss the existence results of the parabolic evolution equation d(x(t) + g(t,x(t)))/dt + A(t)x(t) =f( t ,x(t)) in Banach spaces, where A (t) generates an evolution system and functions f, g are continuous. We get the theorem of existence of a mild solution, the theorem of existence and uniqueness of a mild solution and the theorem of existence and uniqueness of an S-classieal (semi-classical) solution. We extend the cases when g(t) = 0 or A(t) = A.
Ball convergence for Traub-Steffensen like methods in Banach space
Argyros Ioannis K.
2015-12-01
Full Text Available We present a local convergence analysis for two Traub-Steffensen-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. In earlier studies such as [16, 23] Taylor expansions and hypotheses up to the third Fréchet-derivative are used. We expand the applicability of these methods using only hypotheses on the first Fréchet derivative. Moreover, we obtain a radius of convergence and computable error bounds using Lipschitz constants not given before. Numerical examples are also presented in this study.
On the regularity of mild solutions to complete higher order differential equations on Banach spaces
Nezam Iraniparast
2015-09-01
Full Text Available For the complete higher order differential equation u(n(t=Σk=0n-1Aku(k(t+f(t, t∈ R (* on a Banach space E, we give a new definition of mild solutions of (*. We then characterize the regular admissibility of a translation invariant subspace al M of BUC(R, E with respect to (* in terms of solvability of the operator equation Σj=0n-1AjXal Dj-Xal Dn = C. As application, almost periodicity of mild solutions of (* is proved.
ANTI-PERIODIC SOLUTIONS FOR FIRST AND SECOND ORDER NONLINEAR EVOLUTION EQUATIONS IN BANACH SPACES
WEI Wei; XIANG Xiaoling
2004-01-01
In this paper, a new existence theorem of anti-periodic solutions for a class ofstrongly nonlinear evolution equations in Banach spaces is presentedThe equations con-tain nonlinear monotone operators and a nonmonotone perturbationMoreover, throughan appropriate transformation, the existence of anti-periodic solutions for a class of second-order nonlinear evolution equations is verifiedOur abstract results are illustrated by anexample from quasi-linear partial differential equations with time anti-periodic conditionsand an example from quasi-linear anti-periodic hyperbolic differential equations.
Convergence Analysis of Iterative Sequences for a Pair of Mappings in Banach Spaces
Liu Chuan ZENG; N. C. WONG; J. C. YAO
2008-01-01
Let C be a nonempty closed convex subset of a real Banach space E Let S :C→C be a quasi-nonexpansive mapping,let T :C→C be an asymptotically demicontractive and uniformly Lipschitzian mapping,and let F := {x∈C :Sx =x and Tx x }≠φ.Let {xn } n≥0 be the sequence generated from an arbitrary x∈C by xn+1 =(1 -cn) Sxn +cnTnxn,n ≥0 . We prove the necessary and su .cient conditions for the strong convergence of the iterative sequence {xn }to an element of F These extend and improve the recent results of Moore and Nnoli.
Aunyarat Bunyawat
2012-01-01
Full Text Available We introduce an iterative method for finding a common fixed point of a countable family of multivalued quasi-nonexpansive mapping {Ti} in a uniformly convex Banach space. We prove that under certain control conditions, the iterative sequence generated by our method is an approximating fixed point sequence of each Ti. Some strong convergence theorems of the proposed method are also obtained for the following cases: all Ti are continuous and one of Ti is hemicompact, and the domain K is compact.
Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces
Udomene Aniefiok
2006-01-01
Full Text Available Suppose is a nonempty closed convex subset of a real Banach space . Let be two asymptotically quasi-nonexpansive maps with sequences such that and , and . Suppose is generated iteratively by where and are real sequences in . It is proved that (a converges strongly to some if and only if ; (b if is uniformly convex and if either or is compact, then converges strongly to some . Furthermore, if is uniformly convex, either or is compact and is generated by , where , are bounded, are real sequences in such that and , are summable; it is established that the sequence (with error member terms converges strongly to some .
Two-Step Viscosity Approximation Scheme for Variational Inequality in Banach Spaces
Liping Yang
2014-01-01
Full Text Available This paper introduces and analyzes a viscosity iterative algorithm for an infinite family of nonexpansive mappings {Ti}i=1∞ in the framework of a strictly convex and uniformly smooth Banach space. It is shown that the proposed iterative method converges strongly to a common fixed point of {Ti}i=1∞, which solves specific variational inequalities. Necessary and sufficient convergence conditions of the iterative algorithm for an infinite family of nonexpansive mappings are given. Results shown in this paper represent an extension and refinement of the previously known results in this area.
Existence of Solutions to Nonlinear Impulsive Volterra Integral Equations in Banach Spaces
CHEN Fangqi; TIAN Ruilan
2005-01-01
In this paper, the existence of solutions is studied for nonlinear impulsive Volterra integral equations with infinite moments of impulse effect on the half line R+ in Banach spaces.By the use of a new comparison result and recurrence method, the new existence theorems are achieved under a weaker compactness-type condition, which generalize and improve the related results for this class of equations with finite moments of impulse effect on finite interval and infinite moments of impulse effect on infinite interval.
Estimating the number of eigenvalues of linear operators on Banach spaces
Demuth, Michael; Hanauska, Franz; Hansmann, Marcel; Katriel, Guy
2014-01-01
Let $L_0$ be a bounded operator on a Banach space, and consider a perturbation $L=L_0+K$, where $K$ is compact. This work is concerned with obtaining bounds on the number of eigenvalues of $L$ in subsets of the complement of the essential spectrum of $L_0$, in terms of the approximation numbers of the perturbing operator $K$. Our results can be considered as wide generalizations of classical results on the distribution of eigenvalues of compact operators, which correspond to the case $L_0=0$....
Some fixed point theorems for multivalued maps in ordered Banach spaces and applications
Zhai Chengbo
2005-01-01
Full Text Available The existence of maximal and minimal fixed points for various set-valued operators is discussed. This paper presents some new fixed point theorems in ordered Banach spaces. A necessary and sufficient condition for the existence of the fixed point to a class of multivalued maps has been obtained. The uniqueness of the positive fixed point has been discussed. The results extend and improve the corresponding results. As an application, we utilize the results to study the existence and uniqueness of positive fixed points for a class of convex operators. In the end, we give a simple application to certain integral equations.
On growth and covering theorems of quasi-convex mappings in the unit ball of a complex Banach space
张文俊; 刘太顺
2002-01-01
A class of biholomorphic mappings named "quasi-convex mapping" is introduced in the unitball of a complex Banach space. It is proved that this class of mappings is a proper subset of the class ofstarlike mappings and contains the class of convex mappings properly, and it has the same growth and coveringtheorems as the convex mappings. Furthermore, when the Banach space is confined to Cn, the "quasi-convexmapping" is exactly the "quasi-convex mapping of type A" introduced by K. A. Roper and T. J. Suffridge.
Wangkeeree Rabian
2010-01-01
Full Text Available For a countable family of strictly pseudo-contractions, a strong convergence of viscosity iteration is shown in order to find a common fixed point of in either a p-uniformly convex Banach space which admits a weakly continuous duality mapping or a p-uniformly convex Banach space with uniformly Gâteaux differentiable norm. As applications, at the end of the paper we apply our results to the problem of finding a zero of accretive operators. The main result extends various results existing in the current literature.
Yu Wen WANG; Jian ZHANG; Yun An CUI
2012-01-01
Let X,Y be Banach spaces and M be a linear subspace in X × Y ={{x,y}|x ∈ X,y ∈ Y}.We may view M as a multi-valued linear operator from X to Y by taking M(x) ={y|{x,y} ∈ M}.In this paper,we give several criteria for a single-valued operator from Y to X to be the metric generalized inverse of the multi-valued linear operator M.The principal tool in this paper is also the generalized orthogonal decomposition theorem in Banach spaces.
Null controllability and the algebraic Riccati equation in Banach Spaces
Van Neerven, J.M.A.M.
2005-01-01
By a recent result of Priola and Zabczyk, a null controllable linear system [y'(t) = Ay(t) + Bu(t)] in a Hilbert space E is null controllable with vanishing energy if and only if it is null controllable and the only positive self-adjoint solution of the associated algebraic Riccati equation [XA + A*
Convexity conditions and normal structure of Banach spaces
Saejung, Satit
2008-08-01
We prove that F-convexity, the property dual to P-convexity of Kottman, implies uniform normal structure. Moreover, in the presence of the WORTH property, normal structure follows from a weaker convexity condition than F-convexity. The latter result improves the known fact that every uniformly nonsquare space with the WORTH property has normal structure.
On Generic Well-posedness of Restricted Chebyshev Center Problems in Banach Spaces
Chong LI; Genaro LOPEZ
2006-01-01
Let (B) (resp.(K), (B)(l), (k)(l))denote the set of all nonempty bounded(resp. compact, bounded convex, compact convex)closed subsets of the Banach space X, endowed with the Hausdorff metric, and let G be a nonempty relatively weakly compact closed subset of X.Let (b)o stand for the set of all F ∈(b) such that the problem(F,G)is well-posed. We proved that, if X is strictly convex and Kadec, the set (K) (L) (n) (Bo) is a dense Gб-subset of (k)(l)\\G. Furthermore, if X is a uniformly convex Banach space, we will prove more, namely that the set (B)\\(Bo) (resp.(K)\\(Bo), (B)(l)\\(Bo), (K)(L)\\(Bo) is σ-porous in (B) (resp.(K), (B)(L),(K)(L)). Moreover, we prove that for most (in the sense of the Baire category) closed bounded subsets G of X, the set (K)\\(Bo) is dense and uncountable in (K).
Meng Wen
2012-01-01
Full Text Available We introduce a new iterative scheme with Meir-Keeler contractions for an asymptotically nonexpansive mapping in -uniformly smooth and strictly convex Banach spaces. We also proved the strong convergence theorems of implicit and explicit schemes. The results obtained in this paper extend and improve many recent ones announced by many others.
Tian Zhou XU; John Michael RASSIAS; Wan Xin XU
2012-01-01
In this paper,we establish a general solution and the generalized Hyers-Ulam-Rassias stability of the following general mixed additive-cubic functional equation f(kx + y) + f(kx - y) =kf(x + y) + kf(x - y) + 2f(kx) - 2kf(x)in the quasi-Banach spaces.
无
2010-01-01
This paper investigates the existence and multiplicity of nonnegative solutions to a singular nonlinear boundary value problem of second order differential equations with integral boundary conditions in a Banach space. The arguments are based on the construction of a nonempty bounded open convex set and fixed point index theory. Our nonlinearity possesses singularity and first derivative which makes it different with that in [10].
Tuyen Truong
2011-01-01
Full Text Available Abstract We study the strong convergence of a regularization proximal point algorithm for finding a common fixed point of a finite family of nonexpansive mappings in a uniformly convex and uniformly smooth Banach space. 2010 Mathematics Subject Classification: 47H09; 47J25; 47J30.
S. Marshal Anthoni
2004-01-01
Full Text Available We study the existence of mild solutions of the nonlinear second-order neutral functional differential and integrodifferential inclusions with nonlocal conditions in Banach spaces. The results are obtained by using the theory of strongly continuous cosine families of bounded linear operators and a fixed point theorem for condensing maps due to Martelli.
Xingqiu ZHANG
2012-01-01
The existence of positive solutions to a boundary value problem of second-order impulsive singular integro-differential equation with integral boundary conditions in a Banach space is obtained by means of fixed point theory.Moreover,an application is also given to illustrate the main result.
Algebraic Reflexivity of the set of n-Isometries on C(X,E)
Abubaker, A B
2012-01-01
We prove that if the group of isometries of C(X,E) is algebraically reflexive, then the group of n-isometries is also algebraically reflexive. Here, X is a compact Hausdorff space and E is a uniformly convex Banach space such that the group of isometries of E is algebraically reflexive. As a corollary to this, we establish the algebraic reflexivity of the set of generalized bi-circular projections on C(X,E).
THE EXISTENCE OF RADIAL LIMITS OF ANALYTIC FUNCTIONS IN BANACH SPACES
无
2001-01-01
Let X be a complex Banach space without the analytic Radon-Nikodym property. The author shows that G = {f ∈ H∞(D,X): there exists e ＞ 0, such that for almost all θ ∈ [0, 2π], limsup ‖f(rei) - f(sei)‖ ＞ ∈ } is a dense open subset of H (D, X). It is also shown r,s↑1 that for every open subset B of T, there exists F ∈ H∞(D,X), such that F has boundary values everywhere on Bc and F has radial limits nowhere on B. When A is a measurable subset of T with positive measure, there exists f ∈ H∞(D, X), such that f has nontangential limits almost eyerywhere on Ac and f has radial limits almost nowhere on A.
On Quadratic Scalarization of One Class of Vector Optimization Problems in Banach Spaces
V. M. Bogomaz
2012-01-01
Full Text Available We study vector optimization problems in partially ordered Banach Spaces. We suppose that the objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. We discuss the ”classical” scalarization of vector optimization problems in the form of weighted sum and also we propose other type of scalarization for vector optimization problem, the socalled adaptive scalarization, which inherits some ideas of Pascoletti-Serafini approach. As a result, we show that the scalar nonlinear optimization problems can byturn approximated by the quadratic minimization problems. The advantage of such regularization is especially interesting from a numerical point of view because it gives a possibility to apply rather simple computational methods for the approximation of the whole set of efficient solutions.
A Banach space-valued ergodic theorem for amenable groups and applications
Pogorzelski, Felix
2012-01-01
In this paper we study unimodular amenable groups. The first part is devoted to results on the existence of uniform families of quasi tilings for these groups. In light of that, constructions of Ornstein and Weiss are extended by quantitative estimates for the covering properties of the corresponding decompositions. Afterwards, we apply the developed methods to obtain an abstract ergodic theorem for a class of functions mapping subsets of the group into some Banach space. Moreover, applications of this convergence result are studied: the uniform existence of the integrated density of states (IDS) for operators on amenable Cayley graphs; the uniform existence of the IDS for operators on discrete structures being quasi-isometric to some amenable group; the approximation of L2-Betti numbers on cellular CW-complexes; the existence of certain densities of clusters in a percolated Cayley graph.
Linear Impulsive Periodic System with Time-Varying Generating Operators on Banach Space
Wei W
2007-01-01
Full Text Available A class of the linear impulsive periodic system with time-varying generating operators on Banach space is considered. By constructing the impulsive evolution operator, the existence of -periodic -mild solution for homogeneous linear impulsive periodic system with time-varying generating operators is reduced to the existence of fixed point for a suitable operator. Further the alternative results on -periodic -mild solution for nonhomogeneous linear impulsive periodic system with time-varying generating operators are established and the relationship between the boundness of solution and the existence of -periodic -mild solution is shown. The impulsive periodic motion controllers that are robust to parameter drift are designed for a given periodic motion. An example given for demonstration.
Schöpfer, F.; Schuster, T.; Louis, A. K.
2008-10-01
The split feasibility problem (SFP) consists of finding a common point in the intersection of finitely many convex sets, where some of the sets arise by imposing convex constraints in the range of linear operators. We are concerned with its solution in Banach spaces. To this end we generalize the CQ algorithm of Byrne with Bregman and metric projections to obtain an iterative solution method. In case the sets projected onto are contaminated with noise we show that a discrepancy principle renders this algorithm a regularization method. We measure the distance between convex sets by local versions of the Hausdorff distance, which in contrast to the standard Hausdorff distance allow us to measure the distance between unbounded sets. Hereby we prove a uniform continuity result for both kind of projections. The performance of the algorithm is demonstrated with some numerical experiments.
Models of CT dose profiles in Banach space; with applications to CT Dosimetry
Weir, Victor J
2015-01-01
This paper consists of two parts.In the first part, the scatter components of computed tomograpahy dose profiles are modeled using various functions including the solution to Riccati's differential equation. These scatter functions are combined with primary components such as a trapezoidal function and a constructed function that uses the analytic continuation of Heaviside step function. A mathematical theory is developed in Banach space. The modeled function, which is the product of the scatter and primary functions, is used to accurately fit data from the O-arm cone beam imaging system. In a second part of the paper, an approach to dosimtery is developed that shows that the results obtained from the use of a pencil shaped ion chamber is equivalent to that from a farmer chamber. This result is verified by presenting some preliminary experimental data measured in a 64 slice Siemens Sensation scanner.
Ezzinbi, Khalil; Ndambomve, Patrice
2016-01-01
In this work, we consider the control system governed by some partial functional integrodifferential equations with finite delay in Banach spaces. We assume that the undelayed part admits a resolvent operator in the sense of Grimmer. Firstly, some suitable conditions are established to guarantee the existence and uniqueness of mild solutions for a broad class of partial functional integrodifferential infinite dimensional control systems. Secondly, it is proved that, under generally mild conditions of cost functional, the associated Lagrange problem has an optimal solution, and that for each optimal solution there is a minimizing sequence of the problem that converges to the optimal solution with respect to the trajectory, the control, and the functional in appropriate topologies. Our results extend and complement many other important results in the literature. Finally, a concrete example of application is given to illustrate the effectiveness of our main results.
Hybrid methods for accretive variational inequalities involving pseudocontractions in Banach spaces
Chen Rudong
2011-01-01
Full Text Available Abstract We use strongly pseudocontractions to regularize a class of accretive variational inequalities in Banach spaces, where the accretive operators are complements of pseudocontractions and the solutions are sought in the set of fixed points of another pseudocontraction. In this paper, we consider an implicit scheme that can be used to find a solution of a class of accretive variational inequalities. Our results improve and generalize some recent results of Yao et al. (Fixed Point Theory Appl, doi:10.1155/2011/180534, 2011 and Lu et al. (Nonlinear Anal, 71(3-4, 1032-1041, 2009. 2000 Mathematics subject classification 47H05; 47H09; 65J15
Hyperreflexivity of Operator Algebras of the Banach Space%Banach空间上算子代数的超自反性
袁国常; 覃黎明
2005-01-01
In this paper, we introduced the hyperreflexivity of operator algebra A on Banach space, discussed the necessary, and sufficient condition that A is hyperreflexive, the estimate of hyperreflexive constant and the invariance of hyperreflexivety under the similarity transformation.
On the p-Asplund Space of a Banach Space%Banach空间的p-Asplund伴随空间
程立新
2001-01-01
我们称一个定义在Banach空间E上的连续凸函数f具有Frechet可微性质(FDP),如果E上的每个实值凸函数g≤f均在E的一个稠密的Gδ-子集上Frechet可微.本文主要证明了:对任何Banach空间E,均存在一个局部凸的相容拓扑p使得1)(E,p)是Hausdorff局部凸空间;2)E上的每个范数连续具有FDP的凸函数均是p-连续的;3)每个p-连续的凸函数均具有FDP;4)p等价某个范数拓扑当且仅当E是Asplund空间.%Recently, a sequence of articles studied the Frechet differentiability property of convex functions on general Banach spaces and even on topological linear spaces. Cheng et al introduced the notion of the FDP (Frechet differentiability property) of convex functions: an extended real valued proper convex function f on a Banach space E is said to have the FDP if every continuous convex function g with g≤f on E is Frechet differentiable on a dense Gδ subset of E. This paper mainly shows that all such continuous convex functions f on the space E are exactly all continuous convex functions on a locally convex space (E, τ) for some suitably locally convex topology τ, that the space (E, τ) is normable if and only if E is an Asplund space. It also presents a revised version of the main theorems of Cheng et al.
Banach空间一致凸的几个等价定理%Some Equivalent Propositions about Uniformly Convexin Banach Space
刘龙珍
2012-01-01
在一致凸和严格凸Banach空间定义的基础上，给出了Banach空间一致凸的几个等价定理，并由一致凸Banach空间得出几个等价结论。%Basing on the definition of uniformly and strictly convex in Banach space, this paper gives proof of some equivalences of the uniformly convex in the Banach space, drawing serval equivalent conclusions.
Mixed gradient-Tikhonov methods for solving nonlinear ill-posed problems in Banach spaces
Margotti, Fábio
2016-12-01
Tikhonov regularization is a very useful and widely used method for finding stable solutions of ill-posed problems. A good choice of the penalization functional as well as a careful selection of the topologies of the involved spaces is fundamental to the quality of the reconstructions. These choices can be combined with some a priori information about the solution in order to preserve desired characteristics like sparsity constraints for example. To prove convergence and stability properties of this method, one usually has to assume that a minimizer of the Tikhonov functional is known. In practical situations however, the exact computation of a minimizer is very difficult and even finding an approximation can be a very challenging and expensive task if the involved spaces have poor convexity or smoothness properties. In this paper we propose a method to attenuate this gap between theory and practice, applying a gradient-like method to a Tikhonov functional in order to approximate a minimizer. Using only available information, we explicitly calculate a maximal step-size which ensures a monotonically decreasing error. The resulting algorithm performs only finitely many steps and terminates using the discrepancy principle. In particular the knowledge of a minimizer or even its existence does not need to be assumed. Under standard assumptions, we prove convergence and stability results in relatively general Banach spaces, and subsequently, test its performance numerically, reconstructing conductivities with sparsely located inclusions and different kinds of noise in the 2D electrical impedance tomography.
Wang Xiong-rui; Quan Jing; Ji You-qing
2015-01-01
The purpose of this article is to introduce a class of total quasi-ϕ-asymptotically nonexpansive nonself mappings. Strong convergence theorems for common fixed points of a countable family of total quasi-ϕ-asymptotically nonexpan-sive mappings are established in the framework of Banach spaces based on modified Halpern and Mann-type iteration algorithm. The main results presented in this arti-cle extend and improve the corresponding results of many authors.
Hehua Jiao
2014-01-01
Full Text Available In this paper, a new class of semilocal E-preinvex and related maps in Banach spaces is introduced for a nondiﬀerentiable vector optimization problem with restrictions of inequalities and some of its basic properties are studied. Furthermore, as its applications, some optimality conditions and duality results are established for a nondiﬀerentiable vector optimization under the aforesaid maps assumptions.
Kaewkhao A
2010-01-01
Full Text Available Let be a nonempty compact convex subset of a uniformly convex Banach space , and let and be a single-valued nonexpansive mapping and a multivalued nonexpansive mapping, respectively. Assume in addition that and for all . We prove that the sequence of the modified Ishikawa iteration method generated from an arbitrary by , , where and , are sequences of positive numbers satisfying , , converges strongly to a common fixed point of and ; that is, there exists such that .
Li WEI; Rui Lin TAN; Hai Yun ZHOU
2011-01-01
In this paper, we introduce a new iterative scheme for finding the common element of the set of solutions of an equilibrium problem, the set of solutions of variational inequalities for an e-inversely strongly monotone operator and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and 2-uniformly convex Banach space. Some weak convergence theorems are obtained, to extend the previous work.
Cosso, Andrea; Russo, Francesco
2016-11-01
Functional Itô calculus was introduced in order to expand a functional F(t,Xṡ+t,Xt) depending on time t, past and present values of the process X. Another possibility to expand F(t,Xṡ+t,Xt) consists in considering the path Xṡ+t = {Xx+t,x ∈ [-T, 0]} as an element of the Banach space of continuous functions on C([-T, 0]) and to use Banach space stochastic calculus. The aim of this paper is threefold. (1) To reformulate functional Itô calculus, separating time and past, making use of the regularization procedures which match more naturally the notion of horizontal derivative which is one of the tools of that calculus. (2) To exploit this reformulation in order to discuss the (not obvious) relation between the functional and the Banach space approaches. (3) To study existence and uniqueness of smooth solutions to path-dependent partial differential equations which naturally arise in the study of functional Itô calculus. More precisely, we study a path-dependent equation of Kolmogorov type which is related to the window process of the solution to an Itô stochastic differential equation with path-dependent coefficients. We also study a semilinear version of that equation.
郭铁信
1996-01-01
A deep representation theorem of random conjugate spaces and its several important applications are given. As an application of the representation theorem, the following basic theorem is also proved: let B* be the conjugate space of a Banach space B, be a given probability space. Then every B*-valued w*-u-measurable function defined on is w*-equivalent to a B*-valued u-measurable function defined on if and only if B* has the Radon-Nikodym property with respect to
Common Fixed Points for Asymptotic Pointwise Nonexpansive Mappings in Metric and Banach Spaces
P. Pasom
2012-01-01
Full Text Available Let C be a nonempty bounded closed convex subset of a complete CAT(0 space X. We prove that the common fixed point set of any commuting family of asymptotic pointwise nonexpansive mappings on C is nonempty closed and convex. We also show that, under some suitable conditions, the sequence {xk}k=1∞ defined by xk+1=(1-tmkxk⊕tmkTmnky(m-1k, y(m-1k=(1-t(m-1kxk⊕t(m-1kTm-1nky(m-2k,y(m-2k=(1-t(m-2kxk⊕t(m-2kTm-2nky(m-3k,…,y2k=(1-t2kxk⊕t2kT2nky1k,y1k=(1-t1kxk⊕t1kT1nky0k,y0k=xk, k∈N, converges to a common fixed point of T1,T2,…,Tm where they are asymptotic pointwise nonexpansive mappings on C, {tik}k=1∞ are sequences in [0,1] for all i=1,2,…,m, and {nk} is an increasing sequence of natural numbers. The related results for uniformly convex Banach spaces are also included.
E. U. Ofoedu
2009-01-01
a new iterative sequence for a countably infinite family of m-accretive mappings and prove strong convergence of the sequence to a common zero of these operators in uniformly convex real Banach space. Consequently, we obtain strong convergence theorems for a countably infinite family of pseudocontractive mappings. Our theorems extend and improve some important results which are announced recently by various authors.
Songnian He
2012-01-01
Full Text Available Let C be a nonempty closed convex subset of a real uniformly smooth Banach space X, {Tk}k=1∞:C→C an infinite family of nonexpansive mappings with the nonempty set of common fixed points ⋂k=1∞Fix(Tk, and f:C→C a contraction. We introduce an explicit iterative algorithm xn+1=αnf(xn+(1-αnLnxn, where Ln=∑k=1n(ωk/snTk,Sn=∑k=1nωk, and wk>0 with ∑k=1∞ωk=1. Under certain appropriate conditions on {αn}, we prove that {xn} converges strongly to a common fixed point x* of {Tk}k=1∞, which solves the following variational inequality: 〈x*-f(x*,J(x*-p〉≤0, p∈⋂k=1∞Fix(Tk, where J is the (normalized duality mapping of X. This algorithm is brief and needs less computational work, since it does not involve W-mapping.
Approximating fixed points of non-self asymptotically nonexpansive mappings in Banach spaces
Yongfu Su
2006-01-01
Full Text Available Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T:K→E be an asymptotically nonexpansive mapping with {kn}⊂[1,∞ such that ∑n=1∞(kn−1<∞ and F(T is nonempty, where F(T denotes the fixed points set of T. Let {αn}, {αn'}, and {αn''} be real sequences in (0,1 and ε≤αn,αn',αn''≤1−ε for all n∈ℕ and some ε>0. Starting from arbitrary x1∈K, define the sequence {xn} by x1∈K, zn=P(αn''T(PTn−1xn+(1−αn''xn, yn=P(αn'T(PTn−1zn+(1−αn'xn, xn+1=P(αnT(PTn−1yn+(1−αnxn. (i If the dual E* of E has the Kadec-Klee property, then { xn} converges weakly to a fixed point p∈F(T; (ii if T satisfies condition (A, then {xn} converges strongly to a fixed point p∈F(T.
Tomonari Suzuki
2006-06-01
Full Text Available We prove Browder's type strong convergence theorems for infinite families of nonexpansive mappings. One of our main results is the following: let C be a bounded closed convex subset of a uniformly smooth Banach space E. Let {Tn:nÃ¢ÂˆÂˆÃ¢Â„Â•} be an infinite family of commuting nonexpansive mappings on C. Let {ÃŽÂ±n} and {tn} be sequences in (0,1/2 satisfying limntn=limnÃŽÂ±n/tnÃ¢Â„Â“=0 for Ã¢Â„Â“Ã¢ÂˆÂˆÃ¢Â„Â•. Fix uÃ¢ÂˆÂˆC and define a sequence {un} in C by un=(1Ã¢ÂˆÂ’ÃŽÂ±n((1Ã¢ÂˆÂ’Ã¢ÂˆÂ‘k=1ntnkT1un+Ã¢ÂˆÂ‘k=1ntnkTk+1un+ÃŽÂ±nu for nÃ¢ÂˆÂˆÃ¢Â„Â•. Then {un} converges strongly to Pu, where P is the unique sunny nonexpansive retraction from C onto Ã¢ÂˆÂ©n=1Ã¢ÂˆÂžF(Tn.
J. W. Kitchen
1994-01-01
Full Text Available We study bundles of Banach algebras π:A→X, where each fiber Ax=π−1({x} is a Banach algebra and X is a compact Hausdorff space. In the case where all fibers are commutative, we investigate how the Gelfand representation of the section space algebra Γ(π relates to the Gelfand representation of the fibers. In the general case, we investigate how adjoining an identity to the bundle π:A→X relates to the standard adjunction of identities to the fibers.
Dynamical Systems Method (DSM) for solving nonlinear operator equations in Banach spaces
Ramm, A G
2010-01-01
Let $F(u)=h$ be an operator equation in a Banach space $X$, $\\|F'(u)-F'(v)\\|\\leq \\omega(\\|u-v\\|)$, where $\\omega\\in C([0,\\infty))$, $\\omega(0)=0$, $\\omega(r)>0$ if $r>0$, $\\omega(r)$ is strictly growing on $[0,\\infty)$. Denote $A(u):=F'(u)$, where $F'(u)$ is the Fr\\'{e}chet derivative of $F$, and $A_a:=A+aI.$ Assume that (*) $\\|A^{-1}_a(u)\\|\\leq \\frac{c_1}{|a|^b}$, $|a|>0$, $b>0$, $a\\in L$. Here $a$ may be a complex number, and $L$ is a smooth path on the complex $a$-plane, joining the origin and some point on the complex $a-$plane, $00$ is a small fixed number, such that for any $a\\in L$ estimate (*) holds. It is proved that the DSM (Dynamical Systems Method) \\bee \\dot{u}(t)=-A^{-1}_{a(t)}(u(t))[F(u(t))+a(t)u(t)-f],\\quad u(0)=u_0,\\ \\dot{u}=\\frac{d u}{dt}, \\eee converges to $y$ as $t\\to +\\infty$, where $a(t)\\in L,$ $F(y)=f$, $r(t):=|a(t)|$, and $r(t)=c_4(t+c_2)^{-c_3}$, where $c_j>0$ are some suitably chosen constants, $j=2,3,4.$ Existence of a solution $y$ to the equation $F(u)=f$ is assumed. It is also assu...
Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in banach spaces
2006-01-01
Full Text Available Suppose K is a nonempty closed convex subset of a real Banach space E . Let S,T:K→K be two asymptotically quasi-nonexpansive maps with sequences { u n },{ v n }⊂[ 0,∞ such that ∑ n=1 ∞ u n <∞ and ∑ n=1 ∞ v n <∞ , and F=F( S ∩F( T :={ x∈K:Sx=Tx=x }≠φ . Suppose { x n } is generated iteratively by x 1 ∈K, x n+1 =( 1− α n x n + α n S n [ ( 1− β n x n + β n T n x n ],n≥1 where { α n } and { β n } are real sequences in [ 0,1 ] . It is proved that (a { x n } converges strongly to some x ∗ ∈F if and only if lim inf n→∞ d( x n ,F =0 ; (b if X is uniformly convex and if either T or S is compact, then { x n } converges strongly to some x ∗ ∈F . Furthermore, if X is uniformly convex, either T or S is compact and { x n } is generated by x 1 ∈K, x n+1 = α n x n + β n S n [ α ′ n x n + β ′ n T n x n + γ ′ n z ′ n ]+ γ n z n ,n≥1 , where { z n } , { z ′ n } are bounded, { α n },{ β n },{ γ n },{ α ′ n },{ β ′ n },{ γ ′ n } are real sequences in [ 0,1 ] such that α n + β n + γ n =1= α ′ n + β ′ n + γ ′ n and { γ n } , { γ ′ n } are summable; it is established that the sequence { x n } (with error member terms converges strongly to some x ∗ ∈F .
Benedetto BONGIORNO; Luisa DI PIAZZA; Kazimierz MUSIAL
2012-01-01
Let X be a Banach space with a Schauder basts {en},and let Φ(Ⅰ) =∑∞n=1 en ∫I fn(t)dt be a finitely additive interval measure on the unit interval [0,1],where the integrals are taken in the sense of Henstock-Kurzweil.Necessary and sufficient conditions are given for Φ to be the indefinite integral of a Henstock-Kurzweil-Pettis (or Henstock,or variational Henstock) integrable function f:[0,1] → X.
Shisheng ZHANG; Lin WANG; Yunhe ZHAO
2013-01-01
The purpose of this article is first to introduce the concept of multi-valued totally Quasi-φ-asymptotically nonexpansive semi-groups,which contains many kinds of semigroups as its special cases,and then to modify the Halpern-Mann-type iteration algorithm for multi-valued totally Quasi-φ-asymptotically nonexpansive semi-groups to have the strong convergence under a limit condition only in the framework of Banach spaces.The results presented in this article improve and extend the corresponding results announced by many authors recently.
Li Shan LIU
2001-01-01
In this paper, we will prove that Ky Fan's Theorem (Math. Z. 112(1969), 234-240) is true for1-set-contractive maps defined on a bounded closed convex subset K in a Banach space with intK ≠φ.This class of 1-set-contractive maps includes condensing maps, nonexpansive maps, semicontractivemaps, LANE maps and others. As applications of our theorems, some fixed point theorems of non-self-maps are proved under various well-known boundary conditions. Our results are generalizations andimprovements of the recent results obtained by many authors.
Xie-ping DING; Zhong-bao WANG
2009-01-01
A new system of the set-valued mixed quasi-variational-like inclusions (SS-MQVLI) involving H-η-monotone operators is studied in general Banach spaces without uniform smoothness. By using the resolvent operator technique of H-η-monotone opera-tors, a new iterative algorithm for finding approximate solutions to SSMQVLI is proposed. It is shown that the iterative sequences generated by the algorithm converge strongly to the exact solution of SSMQVLI under appropriate assumptions. These obtained new re-sults have extended and improved previous results.
Gang CAI; Shangquan BU
2013-01-01
In this paper,we introduce two new iterative algorithms for finding a common element of the set of solutions of a general equilibrium problem and the set of solutions of the variational inequality for an inverse-strongly monotone operator and the set of common fixed points of two infinite families of relatively nonexpansive mappings or the set of common fixed points of an infinite family of relatively quasi-nonexpansive mappings in Banach spaces.Then we study the weak convergence of the two iterative sequences.Our results improve and extend the results announced by many others.
Narin Petrot
2009-01-01
Full Text Available We prove some strong convergence theorems for fixed points of modified Ishikawa and Halpern iterative processes for a countable family of hemi-relatively nonexpansive mappings in a uniformly convex and uniformly smooth Banach space by using the hybrid projection methods. Moreover, we also apply our results to a class of relatively nonexpansive mappings, and hence, we immediately obtain the results announced by Qin and Su's result (2007, Nilsrakoo and Saejung's result (2008, Su et al.'s result (2008, and some known corresponding results in the literatures.
Wei-Qi Deng
2013-01-01
Full Text Available Let be a nonempty, closed, and convex subset of a real uniformly convex Banach space . Let and be two infinite families of asymptotically nonexpansive mappings from to itself with . For an arbitrary initial point , is defined as follows: , , , where and with and satisfying the positive integer equation: , ; and are two countable subsets of and respectively; , , , , , and are sequences in for some , satisfying and . Under some suitable conditions, a strong convergence theorem for common fixed points of the mappings and is obtained. The results extend those of the authors whose related researches are restricted to the situation of finite families of asymptotically nonexpansive mappings.
Plubtieng Somyot
2009-01-01
Full Text Available Abstract We introduce an iterative scheme for finding a common element of the solution set of a maximal monotone operator and the solution set of the variational inequality problem for an inverse strongly-monotone operator in a uniformly smooth and uniformly convex Banach space, and then we prove weak and strong convergence theorems by using the notion of generalized projection. The result presented in this paper extend and improve the corresponding results of Kamimura et al. (2004, and Iiduka and Takahashi (2008. Finally, we apply our convergence theorem to the convex minimization problem, the problem of finding a zero point of a maximal monotone operator and the complementary problem.
Somyot Plubtieng
2009-01-01
Full Text Available We introduce an iterative scheme for finding a common element of the solution set of a maximal monotone operator and the solution set of the variational inequality problem for an inverse strongly-monotone operator in a uniformly smooth and uniformly convex Banach space, and then we prove weak and strong convergence theorems by using the notion of generalized projection. The result presented in this paper extend and improve the corresponding results of Kamimura et al. (2004, and Iiduka and Takahashi (2008. Finally, we apply our convergence theorem to the convex minimization problem, the problem of finding a zero point of a maximal monotone operator and the complementary problem.
Zhaoli Ma
2012-01-01
Full Text Available We introduce an iterative scheme for finding a common element of the set of solutions of generalized mixed equilibrium problems and the set of fixed points for countable families of total quasi-ϕ-asymptotically nonexpansive mappings in Banach spaces. We prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm in an uniformly smooth and strictly convex Banach space which also enjoys the Kadec-Klee property. The results presented in this paper improve and extend some recent corresponding results.
Pongsakorn Sunthrayuth
2011-01-01
Full Text Available We introduce a new general system of variational inclusions in Banach spaces and propose a new iterative scheme for finding common element of the set of solutions of the variational inclusion with set-valued maximal monotone mapping and Lipschitzian relaxed cocoercive mapping and the set of fixed point of nonexpansive semigroups in a uniformly convex and 2-uniformly smooth Banach space. Furthermore, strong convergence theorems are established under some certain control conditions. As applications, finding a common solution for a system of variational inequality problems and minimization problems is given.
Ranges of bimodule projections and reflexivity
Eleftherakis, G K
2011-01-01
We develop a general framework for reflexivity in dual Banach spaces, motivated by the question of when the weak* closed linear span of two reflexive masa-bimodules is automatically reflexive. We establish an affirmative answer to this question in a number of cases by examining two new classes of masa-bimodules, defined in terms of ranges of masa-bimodule projections. We give a number of corollaries of our results concerning operator and spectral synthesis, and show that the classes of masa-bimodules we study are operator synthetic if and only if they are strong operator Ditkin.
Banach Spaces which are Dual to k Nearly Uniformly Convex Spaces%k接近一致凸空间的对偶空间
苏雅拉图; 乌敦其其格; 包来友
2011-01-01
In this paper, we introduce two new classes of Banach spaces: k nearly uniformly smooth spaces and ω nearly uniformly smooth spaces, which are the dual notions to k nearly uniformly convex spaces and ω nearly uniformly convex spaces respectively, introduced by Denka Kutzarova. We give some characters and properties of these two kinds of Banach spaces. Apart from that we really distinguish the k uniformly smooth spaces, k nearly uniformly smooth spaces, ω nearly uniformly smooth spaces, fully k smooth spaces and nearly uniformly smooth spaces.%该文引入了两类新的Banach空间,即k接近一致光滑空间和ω接近一致光滑空间,它们分别是Denka Kutzarova所引入的k接近一致凸空间和ω接近一致凸空间的对偶空间.作为主要结果,得到了这两类Banach空间的特征刻画及一些性质,弄清了k一致光滑空间、k接近一致光滑空间、ω接近一致光滑空间,完全k光滑空间和接近一致光滑空间的蕴涵关系.
Banach空间的不动点性质%Fixed Point Property in Banach Spaces
吴春雪
2007-01-01
Banach空间中的许多几何性质在不动点理论中起着很重要的作用,其中包括一致凸性,Banach-Saks性质和正规结构等等.文中引入了一个新的几何性质(Ag2)*,通过建立Banach空间X中(Ag2)*性质和Banach-Saks性质及UKK性质、一致Frechet可微的关系,得到的结论是:如果Banach空间X是可分的且其对偶空间X*具有(Ag2)*性质,则X及X*具有弱不动点性质.
M. De la Sen
2013-01-01
Full Text Available Some results on fixed points related to the contractive compositions of bounded operators in a class of complete metric spaces which can be also considered as Banach’s spaces are discussed through the paper. The class of composite operators under study can include, in particular, sequences of projection operators under, in general, oblique projective operators. In this paper we are concerned with composite operators which include sequences of pairs of contractive operators involving, in general, oblique projection operators. The results are generalized to sequences of, in general, nonconstant bounded closed operators which can have bounded, closed, and compact limit operators, such that the relevant composite sequences are also compact operators. It is proven that in both cases, Banach contraction principle guarantees the existence of unique fixed points under contractive conditions.
魏益民; 吴和兵
2001-01-01
We discuss the incomplete semi-iterative method (ISIM) for an approximate solution of a linear fixed point equations x＝ Tx+c with a bounded linear operator T acting on a complex Banach space X such that its resolvent has a pole of order k at the point 1. Sufficient conditions for the convergence of ISIM to a solution of x=Tx+c , where c belongs to the range space of (I-T)k, are established. We show that the ISIM has an attractive feature that it is usually convergent even when the spectral radius of the operator T is greater than 1 and Ind1T≥ 1. Applications in finite Markov chain is considered and illustrative examples are reported, showing the convergence rate of the ISIM is very high.
Boubakari Ibrahimou
2013-01-01
maximal monotone with and . Using the topological degree theory developed by Kartsatos and Quarcoo we study the eigenvalue problem where the operator is a single-valued of class . The existence of continuous branches of eigenvectors of infinite length then could be easily extended to the case where the operator is multivalued and is investigated.
Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces
Aniefiok Udomene
2006-02-01
Full Text Available Suppose K is a nonempty closed convex subset of a real Banach space E. Let S,T:KÃ¢Â†Â’K be two asymptotically quasi-nonexpansive maps with sequences {un},{vn}Ã¢ÂŠÂ‚[0,Ã¢ÂˆÂž such that Ã¢ÂˆÂ‘n=1Ã¢ÂˆÂžun<Ã¢ÂˆÂž and Ã¢ÂˆÂ‘n=1Ã¢ÂˆÂžvn<Ã¢ÂˆÂž, and F=F(SÃ¢ÂˆÂ©F(T:={xÃ¢ÂˆÂˆK:Sx=Tx=x}Ã¢Â‰Â Ã¢ÂˆÂ…. Suppose {xn} is generated iteratively by x1Ã¢ÂˆÂˆK,xn+1=(1Ã¢ÂˆÂ’ÃŽÂ±nxn+ÃŽÂ±nSn[(1Ã¢ÂˆÂ’ÃŽÂ²nxn+ÃŽÂ²nTnxn],nÃ¢Â‰Â¥1 where {ÃŽÂ±n} and {ÃŽÂ²n} are real sequences in [0,1]. It is proved that (a {xn} converges strongly to some xÃ¢ÂˆÂ—Ã¢ÂˆÂˆF if and only if liminfnÃ¢Â†Â’Ã¢ÂˆÂžd(xn,F=0; (b if X is uniformly convex and if either T or S is compact, then {xn} converges strongly to some xÃ¢ÂˆÂ—Ã¢ÂˆÂˆF. Furthermore, if X is uniformly convex, either T or S is compact and {xn} is generated by x1Ã¢ÂˆÂˆK,xn+1=ÃŽÂ±nxn+ÃŽÂ²nSn[ÃŽÂ±Ã¢Â€Â²nxn+ÃŽÂ²Ã¢Â€Â²nTnxn+ÃŽÂ³Ã¢Â€Â²nzÃ¢Â€Â²n]+ÃŽÂ³nzn,nÃ¢Â‰Â¥1, where {zn}, {zÃ¢Â€Â²n} are bounded, {ÃŽÂ±n},{ÃŽÂ²n},{ÃŽÂ³n},{ÃŽÂ±Ã¢Â€Â²n},{ÃŽÂ²Ã¢Â€Â²n},{ÃŽÂ³Ã¢Â€Â²n} are real sequences in [0,1] such that ÃŽÂ±n+ÃŽÂ²n+ÃŽÂ³n=1=ÃŽÂ±Ã¢Â€Â²n+ÃŽÂ²Ã¢Â€Â²n+ÃŽÂ³Ã¢Â€Â²n and {ÃŽÂ³n}, {ÃŽÂ³Ã¢Â€Â²n} are summable; it is established that the sequence {xn} (with error member terms converges strongly to some xÃ¢ÂˆÂ—Ã¢ÂˆÂˆF.
RICCATI EQUATIONS ON NONCOMMUTATIVE BANACH ALGEBRAS
Curtain, Ruth
2011-01-01
Conditions for the existence of a solution of a Riccati equation to be in some prescribed noncommutative involutive Banach algebras are given. The Banach algebras are inverse-closed subalgebras of the space of bounded linear operators on some Hilbert space, and the Riccati equation has an exponentia
Lu-Chuan Ceng
2013-01-01
Full Text Available We introduce and analyze hybrid implicit and explicit extragradient methods for finding a zero of an accretive operator and solving a general system of variational inequalities and a fixed point problem of an infinite family of nonexpansive self-mappings in a uniformly convex Banach space X which has a uniformly Gateaux differentiable norm. We establish some strong convergence theorems for hybrid implicit and explicit extra-gradient algorithms under suitable assumptions. Furthermore, we derive the strong convergence of hybrid implicit and explicit extragradient algorithms for finding a common element of the set of zeros of an accretive operator and the common fixed point set of an infinite family of nonexpansive self-mappings and a self-mapping whose complement is strictly pseudocontractive and strongly accretive in X. The results presented in this paper improve, extend, supplement, and develop the corresponding results announced in the earlier and very recent literature.
Strong Convergence of Cesàro Mean Iterations for Nonexpansive Nonself-Mappings in Banach Spaces
Wangkeeree Rabian
2007-01-01
Full Text Available Let be a real uniformly convex Banach space which admits a weakly sequentially continuous duality mapping from to , a nonempty closed convex subset of which is also a sunny nonexpansive retract of , and a non-expansive nonself-mapping with . In this paper, we study the strong convergence of two sequences generated by and for all , where , is a real sequence in an interval , and is a sunny non-expansive retraction of onto . We prove that and converge strongly to and , respectively, as , where is a sunny non-expansive retraction of onto . The results presented in this paper generalize, extend, and improve the corresponding results of Matsushita and Kuroiwa and many others.
Bekkai Messirdi
2015-03-01
Full Text Available Let X and Y two complex Banach spaces and (A,B a pair of bounded linear operators acting on X with value on Y. This paper is concerned with spectral analysis ofthe pair (A;B: We establish some properties concerning the spectrum of the linear operator pencils (A-lambda B when B is not necessarily invertible and lambda is a complex number. Also, we use the functional calculus for the pair (A,B to prove the corresponding spectral mapping theorem for (A,B. In addition, we define the generalized Kato essential spectrum and the closed range spectra of the pair (A,B and we give some relationships between this spectrums. As application, we describe a spectral analysis of quotient operators.
Normal Structure and Antipodal Points in Banach Spaces%Banach空间的正规结构与对径点
高继
2000-01-01
Let X be a Banach space and S(X)={x∈X, ‖x‖=1} be the unit sphere of X. Four new parameters Jε(X)=sup{βε(x), x∈S(X)}, jε(X)=inf{βε(x), x∈S(X)}, Gε(X)=sup{αε(x),x∈S(X)}, and gε(X)=inf{αε(x),x∈S(X)} where βε(x)=sup{min{‖x+εy‖, ‖x-εy‖, y∈S(X)}}, and αε(x)=inf{max{‖x+εy‖, ‖x-εy‖, y∈S(X)}} 0ε1 and x∈S(X), are introduced and studied. The main result is that a Banach space X with Jε(X)＜1+(ε)/(2), or gε(X)＞1+(ε)/(3) for some 0ε1 has uniform normal structure.%假设S(X)是Banach空间X的单位球面,作者引进了四个新的几何参数:Jε(X)=sup{βε(x), x∈S(X)}, jε(X)=inf{βε(x), x∈S(X)}, Gε(X)=sup{αε(x),x∈S(X)}, gε(X)=inf{αε(x),x∈S(X)}, 其中0ε1,βε(x)=sup{min{‖x+εy‖, ‖x-εy‖, y∈S(X)}}, αε(x)=inf{max{‖x+εy‖, ‖x-εy‖, y∈S(X)}}. 讨论了这些参数的性质. 本文主要结果是:如果有一个ε, 0ε1,使得Jε(X)＜1+(ε)/(2)或gε(X)＞1+(ε)/(3),那末X有一致正规结构.
弱*局部一致凸空间的一些性质%Some Properties of Weak* Locally Uniformly Convex Banach Spaces
高继
2001-01-01
Some equivalent conditions and the properties of Weak* locally uniformly convex Banach spaces are given,and the inheritances of Weak* local uniform convexity in a product and ultraproduct spaces are discussed.%讨论了弱*局部一致凸空间的一些等价定义和性质，以及乘积空间的弱*凸部一致凸的传递性.
Reflexivity: The Creation of Liminal Spaces--Researchers, Participants, and Research Encounters.
Enosh, Guy; Ben-Ari, Adital
2016-03-01
Reflexivity is defined as the constant movement between being in the phenomenon and stepping outside of it. In this article, we specify three foci of reflexivity--the researcher, the participant, and the encounter--for exploring the interview process as a dialogic liminal space of mutual reflection between researcher and participant. Whereas researchers' reflexivity has been discussed extensively in the professional discourse, participants' reflexivity has not received adequate scholarly attention, nor has the promise inherent in reflective processes occurring within the encounter.
Banach空间中的广义非线性混合型拟变分包含%Generalized Nonlinear Mixed Quasi-Variational Inclusion in Banach Spaces
沈自飞; 杨敏波; 程小力
2005-01-01
We consider a new class of generalized mixed quasi variational inclusion problems in Banach spaces. Using the concept of resolvent operator, we suggest an algorithm for solving the generalized nonlinear mixed quasi variational inclusion problems in Banach spaces. Our results improve, generalize and unify some recent results in the literature greatly.%在Banach空间中讨论一类新的广义非线性混合型拟变分包含问题.用预解算子的概念,建立了一种解此类问题的算法.所得结果改进、推广和统一了文献中的一些结果.
Ali Abkar
2017-02-01
Full Text Available In this paper, we introduce an iterative algorithm for solving the split common fixed point problem for a family of multi-valued quasinonexpansive mappings and totally asymptotically strictly pseudocontractive mappings, as well as for a family of totally quasi-ϕ-asymptotically nonexpansive mappings and k-quasi-strictly pseudocontractive mappings in the setting of Banach spaces. Our results improve and extend the results of Tang et al., Takahashi, Moudafi, Censor et al., and Byrne et al.
空间中渐近非扩张型映射的渐近行为%Asymptotic Behavior of Asymptotically Nonexpansive Type Mappings in Banach Space
朱兰萍; 李刚
2009-01-01
Let X be a uniformly convex Banach space X such that its dual X* has the KK property.Let C be a nonempty bounded closed convex subset of X and G be a directed system.Let ={Tt:t ∈G} be a family of asymptotically nonexpansive type mappings on C.In this paper,we investigate the asymptotic behavior of {TtXO:t∈G} and give its weak convergence theorem.
Jinhua Zhu
2012-01-01
finding a common element of the set of solutions for a system of generalized mixed equilibrium problems and the set of common fixed points for a countable family of total quasi-ϕ-asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in an uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in the paper improve and extend some recent results.
Xing Qiu ZHANG
2011-01-01
In this paper,the cone theory and M(o)nch fixed point theorem combined with the monotone iterative technique are used to investigate the positive solutions for a class of systems of nonlinear singular differential equations with multi-point boundary value conditions on the half line in a Banach space.The conditions for the existence of positive solutions are formulated.In addition,an explicit iterative approximation of the solution is also derived.
Some Extensions of Banach's Contraction Principle in Complete Cone Metric Spaces
Raja P
2008-01-01
Full Text Available Abstract In this paper we consider complete cone metric spaces. We generalize some definitions such as -nonexpansive and -uniformly locally contractive functions -closure, -isometric in cone metric spaces, and certain fixed point theorems will be proved in those spaces. Among other results, we prove some interesting applications for the fixed point theorems in cone metric spaces.
Elementary evolutions in Banach algebra
Lindsay, J. Martin; Das, Bata Krishna
2013-01-01
An elementary class of evolutions in unital Banach algebras is obtained by integrating product functions over Guichardet's symmetric measure space on the half-line. These evolutions, along with a useful subclass, are characterised and a Lie-Trotter product formula is proved. The class is rich enough to form the basis for a recent approach to quantum stochastic evolutions.
Anousheh Fatemeh
2015-10-01
Full Text Available Let A be a Banach algebra, E be a Banach A-bimodule and Δ E → A be a bounded Banach A-bimodule homomorphism. It is shown that under some mild conditions, the weakΔ''-amenability of E'' (as an A''-bimodule necessitates weak Δ-amenability of E (as an A-bimodule. Some examples of weak-amenable Banach modules are provided as well.
Strong Convergence of CesÃƒÂ ro Mean Iterations for Nonexpansive Nonself-Mappings in Banach Spaces
Rabian Wangkeeree
2007-10-01
Full Text Available Let E be a real uniformly convex Banach space which admits a weakly sequentially continuous duality mapping from E to E*, C a nonempty closed convex subset of E which is also a sunny nonexpansive retract of E, and T:CÃ¢Â†Â’E a non-expansive nonself-mapping with F(TÃ¢Â‰Â Ã¢ÂˆÂ…. In this paper, we study the strong convergence of two sequences generated by xn+1=ÃŽÂ±nx+(1Ã¢ÂˆÂ’ÃŽÂ±n(1/n+1Ã¢ÂˆÂ‘j=0n(PTjxn and yn+1=(1/n+1Ã¢ÂˆÂ‘j=0nP(ÃŽÂ±ny+(1Ã¢ÂˆÂ’ÃŽÂ±n(TPjyn for all nÃ¢Â‰Â¥0, where x,x0,y,y0Ã¢ÂˆÂˆC, {ÃŽÂ±n} is a real sequence in an interval [0,1], and P is a sunny non-expansive retraction of E onto C. We prove that {xn} and {yn} converge strongly to Qx and Qy, respectively, as nÃ¢Â†Â’Ã¢ÂˆÂž, where Q is a sunny non-expansive retraction of C onto F(T. The results presented in this paper generalize, extend, and improve the corresponding results of Matsushita and Kuroiwa and many others.
Rabian Wangkeeree
2012-01-01
Full Text Available We first prove the existence of solutions for a generalized mixed equilibrium problem under the new conditions imposed on the given bifunction and introduce the algorithm for solving a common element in the solution set of a generalized mixed equilibrium problem and the common fixed point set of finite family of asymptotically nonexpansive mappings. Next, the strong convergence theorems are obtained, under some appropriate conditions, in uniformly convex and smooth Banach spaces. The main results extend various results existing in the current literature.
J. F. Tan
2012-01-01
Full Text Available The main purpose of this paper is by using a hybrid algorithm to find a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for variational inequality problems, and the set of common fixed points for a infinite family of total quasi--asymptotically nonexpansive multivalued mapping in a real uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in this paper improve and extend some recent results announced by some authors.
Banach空间中伪压缩映象不动点的迭代逼近%Approximating Fixed Points of Pseudocontractive Mapping in Banach Spaces
姚永红; 陈汝栋
2008-01-01
Let K be a nonempty closed convex subset of a real p-uniformly convex Banach space E and T be a Lipschitz pseudocontractive self-mapping of K with F(T) := {x ∈K : Tx=x}≠φ.Let a sequence {xn} be generated from x1 ∈K by xn+1 = αnxn+bnTyn+сnun,yn=a'nxn+ b'nTxn+c'nun for all integers n≥1.Then ‖-Txn‖→0 as n→∞.Moreover,if T is completely continuous,then {xn}converges strongly to a fixed point of T.
CONTINUITY AND LINEARITY OF ADDITIVE DERIVATIONS OF NEST ALGEBRAS ON BANACH SPACES
HANDEGUANG
1996-01-01
This paper discusses the problem concerning the continuity and linearity of additive derivation of nest algebras on normed spaces. It is proved that erevy linear derivation of a nest algebra algN is continuous provided that one of the following conditions is satisfied:(1)0+（包含）0.(2)X-（包含于）X.(3)there exists a non-trivial idempotnet p in algN such that the range of p belongs to N, It is also proved that every additive derivation of a nest algebra is automatically linear if the underlying normed space is infinite dimemnsional.
ON SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS BY THE HAHN-BANACH THEOREM
advantageous for domains with general boundaries and for Riemannian manifolds. The proof of the Hahn-Banach theorem in the form used does not require transfinite induction, since the Banach space of continous functions is separable.
Variational Formulas of Poincaré-Type Inequalities in Banach Spaces of Functions on the Line
Mu Fa CHEN
2002-01-01
Motivated from the study on logarithmic Sobolev, Nash and other functional inequalities,spaces of functions on the line. Explicit criteria for the inequalities to hold and explicit estimatesfor the optimal constants in the inequalities are presented. As a typical application, the logarithmicSobolev constant is carefully examined.
Stochastic integration in Banach spaces and applications to parabolic evolution equations
Veraar, M.C.
2006-01-01
Stochastic partial differential equations (SPDEs) of evolution type are usually modelled as ordinary stochastic differential equations (SDEs) in an infinite-dimensional state space. In many examples such as the stochastic heat and wave equation, this viewpoint may lead to existence and uniqueness re
A new approach to investigation of evolution differential equations in Banach spaces
Alber, Y I
1993-01-01
and that $B$ is dense in $H$. The stabilization of solutions of evolution equations has been proven either in the sense of weak convergence in $B$ or in the norm of $H$ space, and only asymptotic estimates of stabilization rate have been obtained [15]. In the present paper we consider equations of type (0.1) without conditions (0.2) and establish stabilization with both
Botelho, Fabio
2014-01-01
This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.
Crossed products of Banach algebras. I
Dirksen, Sjoerd; Wortel, Marten
2011-01-01
We construct a crossed product Banach algebra from a Banach algebra dynamical system $(A,G,\\alpha)$ and a given uniformly bounded class $R$ of continuous covariant Banach space representations of that system. If $A$ has a bounded left approximate identity, and $R$ consists of non-degenerate continuous covariant representations only, then the non-degenerate bounded representations of the crossed product are in bijection with the non-degenerate $R$-continuous covariant representations of the system. This bijection, which is the main result of the paper, is also established for involutive Banach algebra dynamical systems and then yields the well-known representation theoretical correspondence for the crossed product $C^*$-algebra as commonly associated with a $C^*$-algebra dynamical system as a special case. Taking the algebra $A$ to be the base field, the crossed product construction provides, for a given non-empty class of Banach spaces, a Banach algebra with a relatively simple structure and with the property...
无
2000-01-01
The comparison principle is first established,and then the lower and upper solution method and the monotone iterative technique are employed to the study of terminal value problems for the first order nonlinear impulsive integro-differential equations in Banach spaces.Finally,the existence theorem on the maximal and minimal solutions is obtained.
白占立; 姜桅
2012-01-01
It is researched that the equivalent problems of the convergence theorems of modified Mann and Ishikawa iterations with errors in real Banach spaces.%在任意实Banach空间中研究了带误差修改的Mann迭代和Ishikawa迭代收敛的等价性问题.
苏永福
2001-01-01
文[4]把文[3]的主要结果从Hilbert空间推广到一致凸Banach空间,证明了一致凸Banach空间中文上从有界闭凸集到自身的渐近非扩张映象的迭代序列收敛定理.本文将有界闭凸集的条件减弱为闭凸集,从而推广了文[4]的相应结果.%In paper [4], the relative result of Jiirgen schu is extended to a uniformly convex Banach space, and the convergence of iterative sequence in an uniformly conves Banach space for asymptotically non - expanstive mapping is proved.In paper [4], T is asymptotically non - expanstive mapping with sequence {Kn} in a bounded closed convex subset C of uniformly convex Banach space.In this paper, we let only C is closed convex subset of uniformlly convex Banach space. But convergence theorms of iterative sequences for asymptotically non-expanstive mapping was also proved.
Visual suppression of the vestibulo-ocular reflex during space flight
Uri, John J.; Thornton, William E.; Moore, Thomas P.; Pool, Sam L.
1989-01-01
Visual suppression of the vestibulo-ocular reflex was studied in 16 subjects on 4 Space Shuttle missions. Eye movements were recorded by electro-oculography while subjects fixated a head mounted target during active sinusoidal head oscillation at 0.3 Hz. Adequacy of suppression was evaluated by the number of nystagmus beats, the mean amplitude of each beat, and the cumulative amplitude of nystagmus during two head oscillation cycles. Vestibulo-ocular reflex suppression was unaffected by space flight. Subjects with space motion sickness during flight had significantly more nystagmus beats than unaffected individuals. These susceptible subjects also tended to have more nystagmus beats before flight.
Sheng Fan ZHOU; Qiu Li JIA; Wei SHI
2007-01-01
We obtain an estimate of the upper bound for Kolmogorov's ε-entropy for the bounded sets with small "tail" in discrete spaces, then we present a sufficient condition for the existence of a global attractor for dissipative lattice systems in a reflexive Banach discrete space and establish an upper bound of Kolmogorov's ε-entropy of the global attractor for lattice systems.
陈亮; 吐尔德别克
2011-01-01
用Hardy鞅的原子分解刻画了复拟Banach空间的解析(q一致凸性,并用原子分解证明了两个Hardy鞅空间的嵌入关系.%The analytic q-uniform convexity of complex Quasi-Banach space is described by atomic decomposition of Hardy martingales,the embedding relationship between two Hardy martingale spaces is discussed by the method of atomic decomposition.
黄健; 戴正德
2004-01-01
在本文中,我们在Banach空间考虑二维广义Ginzburg-Landau方程的指数吸引子,且得到其分形维度估计.%In this paper, we consider the exponential attractor for the derivative two - dimensional Ginzburg - Landau equation in Banach space Xαp and also obtain the estimation of the fractal dimension.
A generalization of fixed point theorem in 2 -Banach space%2-Banach空间上不动点定理的一个推广
朴勇杰; 沈京虎
2011-01-01
The definition and the relative concepts of a 2 -linear norm are introduced on a linear space and the definition of a class Φ of 5 - dimensional functions on R 5+ is given. A convergent sequence { xn } on a 2 - Banach space is constructed by an involution map T satisfying a class Φ of 5 dimensional functions on R 5+, and then the limit of the sequence { xn } being the fixed point of T is proved. The main result generalizes and improves the corresponding result obtained by M S Hhan and M D Hkan.%介绍了线性空间上的2-线性赋范的定义和相关概念并给出了R5+上的5-元函数类Φ的定义.利用2-Banach空间上满足5-元函数类Φ中的对合映射T构造出一类收敛的序列,并证明了该序列的极限正是T的不动点.主要结果推广和改进了由M S Hhan和M D Hkan得到的相应结果.
Exploring the Gendering of Space by Using Memory Work as a Reflexive Research Method
Lia Bryant
2007-09-01
Full Text Available How can memory work be used as a pathway to reflect on the situatedness of the researcher and field of inquiry? The key aim of this article is to contribute to knowledge about the gendering of space developed by feminist geographers by using memory work as a reflexive research method. The authors present a brief review of feminist literature that covers the local and global symbolic meanings of spaces and the power relations within which space is experienced. From the literature they interpret themes of the interconnections between space, place, and time; sexualization of public space; and the bodily praxis of using space. Memories of gendered bodies and landscapes, movement and restricted space, and the disrupting of space allow the exploration of conceptualizations within the literature as active, situated, fragmented, and contextualized.
Uniformly Convex Metric Spaces
Kell Martin
2014-01-01
In this paper the theory of uniformly convex metric spaces is developed. These spaces exhibit a generalized convexity of the metric from a fixed point. Using a (nearly) uniform convexity property a simple proof of reflexivity is presented and a weak topology of such spaces is analyzed. This topology called co-convex topology agrees with the usualy weak topology in Banach spaces. An example of a $CAT(0)$-spaces with weak topology which is not Hausdorff is given. This answers questions raised b...
El espacio cociente y algunas propiedades geométricas de los espacios de Banach
2009-01-01
We state some geometric properties of Banach spaces, such as uniformly convex spaces, uniformly non-square spaces, local uniformly convex spaces, strictly convex spaces, etc., and we analyze the problem of translating such properties to the quotient space.keywords: uniformly convex sapce, uniformly non-squere sapce, LUR space, (R) space. En esta nota enunciaremos alguans propiedades geométricas de los espacios de Banach, entre las cuales podemos señalar espacios uniformemente convexos, esp...
张石生
2002-01-01
Some necessary and sufficient conditions for convergence of Ishikawa Mann and steepest descent iterative sequence for accretive and pseudo-contractive type mapping in Banech spaces were obtained. The results improve, extend and include some recent results.
李小龙
2012-01-01
The existence of positive solutions for nonlinear Robin boundary value problem in an ordered Banach spaces was discussed. An existence result of positive solutions was obtained by employing a new estimate of noncompactness measure and the fixed point index theory of condensing mapping.%讨论有序Banach空间E中的非线性Robin边值问题正解的存在性,通过非紧性测度的估计技巧与凝聚映射的不动点指数理论获得该问题正解的存在性结果.
刘英; 陈永利; 何震
2008-01-01
In this paper,we first introduce a new class of generalized accretive operators named(H,η)-accretive in Banach space.By studying the properties of(H,η)-accretive,we extend the concept of resolvent operators associated with m-accretive operators to the new(H,η)-accretive operators.In terms of the new resolvent operator technique,we prove the existence and uniqueness of solutions for this new system of variational inclusions.We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm.
Ayupov, Sh A
2011-01-01
In the present article we prove a fixed point theorem for reflections of compact convex sets and give a new characterization of state space of JB-algebras among compact convex sets. Namely they are exactly those compact convex sets which are strongly spectral and symmetric.
Some C∗-algebras which are coronas of non-C∗-Banach algebras
Voiculescu, Dan-Virgil
2016-07-01
We present results and motivating problems in the study of commutants of hermitian n-tuples of Hilbert space operators modulo normed ideals. In particular, the C∗-algebras which arise in this context as coronas of non-C∗-Banach algebras, the connections with normed ideal perturbations of operators, the hyponormal operators and the bidual Banach algebras one encounters are discussed.
Zhang Peiguo
2011-01-01
Full Text Available Abstract By obtaining intervals of the parameter λ, this article investigates the existence of a positive solution for a class of nonlinear boundary value problems of second-order differential equations with integral boundary conditions in abstract spaces. The arguments are based upon a specially constructed cone and the fixed point theory in cone for a strict set contraction operator. MSC: 34B15; 34B16.
Asymptotic aspect of derivations in Banach algebras.
Roh, Jaiok; Chang, Ick-Soon
2017-01-01
We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. We finally take central linear derivations with radical ranges on semiprime Banach algebras and a continuous linear generalized left derivation on a semisimple Banach algebra.
2008-01-01
Let (Ω,A,μ) be a probability space, K the scalar field R of real numbers or C of complex numbers,and (S,X) a random normed space over K with base (Ω,A,μ). Denote the support of (S,X) by E, namely E is the essential supremum of the set {A ∈ A : there exists an element p in S such that Xp(ω) > 0 for almost all ω in A}. In this paper, Banach-Alaoglu theorem in a random normed space is first established as follows: The random closed unit ball S*(1) = {f ∈ S* : Xf* 1} of the random conjugate space (S*,X*) of (S,X) is compact under the random weak star topology on (S*,X*) iff E∩A=: {E∩A | A ∈ A} is essentially purely μ-atomic (namely, there exists a disjoint family {An : n ∈ N} of at most countably many μ-atoms from E∩A such that E =∪n∞=1 An and for each element F in E∩A, there is an H in the σ-algebra generated by {An : n ∈ N} satisfying μ(F △H) = 0), whose proof forces us to provide a key topological skill, and thus is much more involved than the corresponding classical case. Further, Banach-Bourbaki-Kakutani-mulian (briefly, BBKS) theorem in a complete random normed module is established as follows: If (S,X) is a complete random normed module, then the random closed unit ball S(1) = {p ∈ S : Xp 1} of (S,X) is compact under the random weak topology on (S,X) iff both (S,X) is random reflexive and E∩A is essentially purely μ-atomic. Our recent work shows that the famous classical James theorem still holds for an arbitrary complete random normed module, namely a complete random normed module is random reflexive iff the random norm of an arbitrary almost surely bounded random linear functional on it is attainable on its random closed unit ball, but this paper shows that the classical Banach-Alaoglu theorem and BBKS theorem do not hold universally for complete random normed modules unless they possess extremely simple stratification structure, namely their supports are essentially purely μ-atomic. Combining the James theorem and
GUO TieXin
2008-01-01
Let(Ω,A,μ)be a probability space,K the scalar field R of real numbers or C of complex numbers,and(S,X)a random normed space over K with base(Ω,A,μ).Denote the support of(S,X)by E,namely E is the essentiaI supremum of the ser {A∈A:there exists an element p in S such that Xp(ω)＞0 for almost all ω in A}. In this paper,Banach-Alaoglu theorem in a random normed space is first established as follows:The random closed unit ball S*(1)={f∈S*:X*f≤1}of the random conjugate space(S*,x*)of(S,X)is compact under the random weak star topology on (S*,X*)iff E∩A=:{E∩A|A∈A}is essentially purely μ-atomic(namely,there exists a disjoint family{An:n∈N}of at most countably many μ-atoms from E∩A such that E=∪∞n=1 An and for each element F in E∩A,there is an H in the σ-algebra generated by{An:n∈N)satisfying μ(F△H)=0),whose proof forces us to provide a key topological skill,and thus is much more involved than the corresponding classical case.Further,Banach-Bourbaki-Kakutani-Smulian(briefly,BBKS)theorem in a complete random normed module is established as follows:If(S,X)is a complete random normed module,then the random closed unit ball S(1)={p∈S:Xp≤1}of(S,X)is compact under the random weak topology on(S,X)iff both(S,X)is random reflexive and E∩A is essentially purely μ-atomic.Our recent work shows that the famous classical James theorem still holds for an arbitrary complete random normed module,namely a complete random normed module is random reflexive iff the random norm of an arbitrary almost surely bounded random linear functional on it is attainable on its random closed unit ball,but this paper shows that the classical Banach-Alaoglu theorem and BBKS theorem do not hold universally for complete random normed modules unless they possess extremely simple stratification structure,namely their supports are essentially purely μ-atomic.Combining the James theorem and BBKS theorem in complete random normed modules leads directly to an interesting
俞卫琴; 陈芳启
2008-01-01
By the use of Monch fixed point theorem and a new comparison result, the solutions of initial value problems for nonlinear second order impulsive integro-differential equations of mixed type in Banach spaces are investigated and the existence theorem is obtained.
王雄瑞
2011-01-01
In this paper, the author gives some convergence theorems of the sufficient and necessary conditions in determining the convergence of Reich type mean iteration for asymptotically nonexpansive mapping in Banach spaces, such as Hilbert spaces, and some implicit conditions of recent relative papers are deleted.%利用粘性逼近法在Hilbert空间以及lp(1＜p≤2)等空间中给出了判定渐近非扩张非自射映象的Reich均值迭代强收敛的充要条件,并去掉了最近相关文献中的一些复杂条件.
On the convexity and smoothness of Banach space and its application%Banach空间的凸性和光滑性及其应用
方习年
2001-01-01
简要概述国际和国内 Banach空间理论的研究状况 , 综述对 Banach空间的凸性和光滑性所做的工作 : 用线性泛函的函数值作元素构成的行列式、单位球的切片、一致凸定义的形式以及特征函数等形式 ,分别刻划及定义空间的 k- 严格凸、 (局部 )k- 致凸、 k- 强凸、 (局部 )近 - 致凸、近强凸等凸性以及 (局部 )k- 致光滑 , k- 强光滑 (局部 )近 - 致光滑等光滑性 , 并讨论以上空间的关系及性质 ; 给出弱 Banach- Saks性质的新特征 , 引入 B- NUC和 g- NUCε空间概念证明 : 具有 Banach- Saks性质的近 - 致凸空间等价于 B- NUC空间、具有 Banach- Saks性质的 NUCε空间等价于 g- NUCε空间举例说明非 k- NUC空间的 B- NUC空间的存在性 ; 研究近强凸、近非常凸空间的几何性质、拓朴性质 , 并得到 : 近强凸空间中的度量投影具有上半连续性 , 近非常凸空间中的度量投影具有弱上半连续性
Banach格上正则AM-紧算子的AM-空间%AM-space and AL-space of Positive AM-compact Operators on Banach Lattices
程娜; 李曦
2013-01-01
给出Banach格上所有从E到F的正则AM-紧算子空间在・ AM范数下是AL-空间，当且仅当E是AM-空间，且F是AL-空间；正则AM-紧算子空间在・ AM范数下是AM-空间，当且仅当E是AL-空间，F是AM-空间。%It is shown that the space generated by all positive AM-compact operators from E into F, is an AL-space under the・ AM -norm if and only if E is an AM-space and F is an AL-space;the space of all positive AM-compact operators from E into F is an AM-space under ・ AM -norm if and only if E is an AL-space and F is an AM-space.
Derivations into Duals of Ideals of Banach Algebras
M E Gorgi; T Yazdanpanah
2004-11-01
We introduce two notions of amenability for a Banach algebra $\\mathcal{A}$. Let be a closed two-sided ideal in $\\mathcal{A}$, we say $\\mathcal{A}$ is -weakly amenable if the first cohomology group of $\\mathcal{A}$ with coefficients in the dual space * is zero; i.e., $H^1(\\mathcal{A},I^*) =\\{0\\}$, and, $\\mathcal{A}$ is ideally amenable if $\\mathcal{A}$ is -weakly amenable for every closed two-sided ideal in $\\mathcal{A}$. We relate these concepts to weak amenability of Banach algebras. We also show that ideal amenability is different from amenability and weak amenability. We study the -weak amenability of a Banach algebra $\\mathcal{A}$ for some special closed two-sided ideal .
赵吕慧子; 孙经先
2011-01-01
The definition of a class of new operators, convex-power 1-set-contraction operators in Banach spaces is giv en , and the existence of fixed points of this class of operators is studied. By using methods of approximation by opera tors, the fixed point theorems of Rothe and Altman type convex-power 1-set-contraction operators is obtained, which generalize fixed point theorems of 1-set-contraction operators.%在Banach空间中给出了一类新算子——凸幂1集压缩算子的定义,研究了这类新算子不动点的存在性问题,利用算子逼近的方法,获得了Rothe及Altman型凸幂1集压缩算子的不动点定理,推广了1集压缩算子的不动点定理.
Additive Functional Inequalities in Banach Modules
An JongSu
2008-01-01
Full Text Available Abstract We investigate the following functional inequality in Banach modules over a -algebra and prove the generalized Hyers-Ulam stability of linear mappings in Banach modules over a -algebra in the spirit of the Th. M. Rassias stability approach. Moreover, these results are applied to investigate homomorphisms in complex Banach algebras and prove the generalized Hyers-Ulam stability of homomorphisms in complex Banach algebras.
Abbas NAJATI
2009-01-01
In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi-Banach algebras associated with the following Pexiderized Jensen functional equation f(x+y/2+z)-g(x-y/2+z)=h(y).This is applied to investigating homomorphisms between quasi-Banach algebras. The concept of the generalized Hyers-Ulam stability originated from Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soe., 72, 297-300 (1978).
Stability of functional equations in Banach algebras
Cho, Yeol Je; Rassias, Themistocles M; Saadati, Reza
2015-01-01
Some of the most recent and significant results on homomorphisms and derivations in Banach algebras, quasi-Banach algebras, C*-algebras, C*-ternary algebras, non-Archimedean Banach algebras and multi-normed algebras are presented in this book. A brief introduction for functional equations and their stability is provided with historical remarks. Since the homomorphisms and derivations in Banach algebras are additive and R-linear or C-linear, the stability problems for additive functional equations and additive mappings are studied in detail. The latest results are discussed and examined in stability theory for new functional equations and functional inequalities in Banach algebras and C*-algebras, non-Archimedean Banach algebras, non-Archimedean C*-algebras, multi-Banach algebras and multi-C*-algebras. Graduate students with an understanding of operator theory, functional analysis, functional equations and analytic inequalities will find this book useful for furthering their understanding and discovering the l...
Zegeye, Habtu; Shahzad, Naseer
2014-01-01
We introduce an iterative process for finding an element of a common fixed point of a finite family of Bregman weak relatively nonexpansive mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.
Uniformly convex-transitive function spaces
Rambla-Barreno, Fernando; Talponen, Jarno
2009-01-01
We introduce a property of Banach spaces called uniform convex-transitivity, which falls between almost transitivity and convex-transitivity. We will provide examples of uniformly convex-transitive spaces. This property behaves nicely in connection with some Banach-valued function spaces. As a consequence, we obtain new examples of convex-transitive Banach spaces.
Wagon, Stan
1985-01-01
The Banach-Tarski paradox is a most striking mathematical construction: it asserts that a solid ball may be taken apart into finitely many pieces that can be rearranged using rigid motions to form a ball twice as large as the original. This volume explore
Reflexive Aero Structures for Enhanced Survivability Project
National Aeronautics and Space Administration — Cornerstone Research Group Inc. (CRG) proposes to develop an advanced reflexive structure system to increase the survivability of aerostructures. This reflexive...
谷峰
2009-01-01
Let E be a real Banach space and K be a nonempty closed convex and bounded subset of E.Let Ti : K → K,i = 1,2,...,N,be N uniformly L-Lipschitzian,uniformly asymptotically regular with sequences {εn (i)} and asymptotically pseudocontractive mappings with sequences {kn (i)},where {kn (i)} and {εn (i)},i = 1,2,...,N,satisfy certain mild conditions.Let a sequence {xn} be generated from x1 ∈ K by zn:= (1-1μn)xn+μnTnnxn,xn1 := λnθnx1+ [1-λn(1 + θn)]xn + λnTnnzn for all integer n≥ 1,where Tn = Tn(mod N),and {λn},{θn} and {μn} are three real sequences in [0,1] satisfying appropriate conditions.Then ‖xn -Tixn‖→0as n →∞ for each l ∈ {1,2,...,N}.The results presented in this paper generalize and improve the corresponding results of Chidume and Zegeye[1],Reinermann[10],Rhoades[11] and Schu[13].
倪仁兴; 吴阳洋; 陈思佳; 周燕; 王倩; 陈罗丹
2012-01-01
By using generalized hybrid projection algorithms methods, strong convergence results of common solutions for three sets of solutions (those to an equilibrium problem, those to variational inequalities, and those to common fixed points for two closed quassi - φ - nonexpansive mapping) are established in 2 - uniformly convex and uniformly smooth Banach space. These results improve and extend the corresponding results of Matsushita and Takahashi obtained in 2005, Qin, Cho and Kang obtained in 2009.%在一致光滑和2-一致凸Banach空间框架下，引入广义杂交投影算法，建立了该算法强收敛于3个集合（平衡问题的解集、变分不等式的解集和两闭拟Ф-非扩张映射公共不动点集）的公共解的新结果．所得结果本质改进和推广了2005年Matsushita和Takahashi、2009年Qin X L，Cho Y Je和Kang S M等人的相应新结果．
Aileen Collier
2016-05-01
Full Text Available Background: There is international consensus of the need for improved palliative and end-of-life care in hospital settings. What is less clear is how such improvements might be realised in practice. Research and practice improvement methodologies need to acknowledge the relational, spiritual, moral and ethical as well as physical dimensions of death and dying if improvements in care are to be achieved. Aims and objectives: The aim of this article is to explore the potential of video-reflexive ethnography as a practice development methodology to improve care of people with a life-limiting illness in the hospital setting. Methods: The study used video-reflexive ethnography and was underpinned by an indigenous research ethical framework. Findings: Study findings highlight the potential of video-reflexive ethnography as a practice development methodology. The reach of video extended internally and externally beyond immediate practice research sites to make hospital dying tangible. The research acted as a disruptive innovation, foregrounding peoples’ (patients and families expertise as well as that of healthcare workers. For some patient and family participants, the research offered a visual legacy. Conclusions: The theories underpinning video-reflexive ethnography and practice development are closely aligned; the former has potential as a practice development methodology to promote person-centred palliative and end-of-life care. The underpinning philosophical, ethical and values framework through which it is applied, along with the skills and aptitude of facilitation, are critical if its potential is to be realised. Implications for practice development: The delivery of person-centred end-of-life care may be facilitated by: Healthcare workers seeing themselves and those they care for differently Healthcare organisations seeing their employees as well as patients and families differently Researchers also being prepared to see themselves differently
Peterka, Robert J.
Recent studies by Diamond and Markham 1,2 have identified significant correlations between space motion sickness susceptibility and measures of disconjugate torsional eye movements recorded during parabolic flights. These results support an earlier proposal by von Baumgarten and Thümler 3 which hypothesized that an asymmetry of otolith function between the two ears is the cause of space motion sickness. It may be possible to devise experiments that can be performed in the 1 g environment on earth that could identify and quantify the presence of asymmetric otolith function. This paper summarizes the known physiological and anatomical properties of the otolith organs and the properties of the torsional vestibulo-ocular reflex which are relevant to the design of a stimulus to identify otolith asymmetries. A specific stimulus which takes advantage of these properties is proposed.
Wood, Scott J.; Clarke, A. H.; Rupert, A. H.; Harm, D. L.; Clement, G. R.
2009-01-01
Two joint ESA-NASA studies are examining changes in otolith-ocular reflexes and motion perception following short duration space flights, and the operational implications of post-flight tilt-translation ambiguity for manual control performance. Vibrotactile feedback of tilt orientation is also being evaluated as a countermeasure to improve performance during a closed-loop nulling task. Data is currently being collected on astronaut subjects during 3 preflight sessions and during the first 8 days after Shuttle landings. Variable radius centrifugation is utilized to elicit otolith reflexes in the lateral plane without concordant roll canal cues. Unilateral centrifugation (400 deg/s, 3.5 cm radius) stimulates one otolith positioned off-axis while the opposite side is centered over the axis of rotation. During this paradigm, roll-tilt perception is measured using a subjective visual vertical task and ocular counter-rolling is obtained using binocular video-oculography. During a second paradigm (216 deg/s, less than 20 cm radius), the effects of stimulus frequency (0.15 - 0.6 Hz) are examined on eye movements and motion perception. A closed-loop nulling task is also performed with and without vibrotactile display feedback of chair radial position. Data collection is currently ongoing. Results to date suggest there is a trend for perceived tilt and translation amplitudes to be increased at the low and medium frequencies on landing day compared to pre-flight. Manual control performance is improved with vibrotactile feedback. One result of this study will be to characterize the variability (gain, asymmetry) in both otolith-ocular responses and motion perception during variable radius centrifugation, and measure the time course of post-flight recovery. This study will also address how adaptive changes in otolith-mediated reflexes correspond to one's ability to perform closed-loop nulling tasks following G-transitions, and whether manual control performance can be improved
The vestibulo-ocular reflex and its possible roles in space motion sickness
Watt, Douglas G. D.
1987-01-01
Prolonged exposure to an inappropriate vestibulo-ocular reflex (VOR) will usually lead to motion sickness, and it has been predicted on theoretical grounds that VOR gain may be decreased in weightlessness. While experiments during parabolic flight in aircraft tend to confirm this prediction, experiments during orbital spaceflight have led to apparently contradictory results. It is suggested that VOR gain is reduced initially, but that rapid compensatory mechanisms restore it to normal within minutes of reaching weightlessness. However, even though this process may lead to the rapid return of functionally normal gaze stability, it may not protect against the development of motion sickness.
王纯; 潘思明
2011-01-01
In this paper, in order to investigate the convergences of Mann-type iterative scheme for a countable family of strict pseudocontraction mappings in a uniformly convex Banach space with the Frechet differentiable norm, we used the results obtained by Marino-Xu, Zhou, Osilike-Udomene, Zhang-Guo and the corresponding results to ex tend some conclusions obtained by Chidume-Shahzad to the real uniformly convex Banach space with the Frechet dif ferentiable norm under the countable strictly pseudocontraction mappings. And the proof of the weak convergences of Mann-type iterative scheme for a countable family of strict pseudocontraction mappings in this Banach space with the Frechet differentiable norm was given.%为了研究在具有Fréchet可微范数的实一致凸Banach空间中的可数的严格伪压缩映射族Mann型迭代方案的收敛性,利用Marino-Xu,Zhou,Osilike-Udomene,Zhang-Guo的结论以及其它相关的结论,在已有结论的基础上,将Chidume-Shahzad的某些结论推广到具有Fréhet可微范数的实一致凸Banach空间的无限严格伪压缩映射族的情形下,并给出了在具有Fréchet可微范数的实一致凸Banach空间中的可数严格伪压缩映射族的Mann型迭代方案弱收敛性的证明.
AL-space of Positive b-AM-compact Operators on Banach Lattice%Banach格上b-AM-紧算子空间的AL-空间
程娜
2013-01-01
得到了Banach格上所有从E到F的正则b-AM-紧算子空间在‖·‖b-AM-范数下是AL-空间当且仅当E是AM-空间且F是AL-空间.正则b-AM-紧算子空间在‖·‖b-AM-范数下同构于AL-空间当且仅当E同构于AM-空间且F同构于AL-空间.%We present that Krb-AM(E,F),the space of all positive b-AM-compact operators from E into F,is an AL-space under the ‖·‖b-AM-norm if and only if E is an AM-space and F is an AL-space; Krb-AM(E,F) under the ‖·‖b-AM-norm is isomorphic to an AL-space if and only if E is an AM-space and F is an AL-space.
唐玉超; 刘理蔚
2007-01-01
本文研究了在一致凸Banach空间中定义在闭凸集C上渐近非扩张映象T不动点的迭代问题,我们的讨论去掉了在刘和薛[2]中C是有界的假设.%In this paper,we approximate fixed point of asymptotically nonexpansive mapping T on a closed,convex subset C of a uniformly convex Banach space.Our argument removes the boundedness assumption on C,generalizing theorems of Liu and Xue.
周海云; 高改良; 陈东青
2003-01-01
In the present paper, by virtue of new analysis technique, we have established a new strong convergence theorem for the modified Mann iteration scheme for a class of asymptotically nonexpansive mappings in uniformly convex Banach spaces. Our results improve the recent ones announced by Schu, Rhoades and others.%通过使用新的分析技巧,建立了(关于)渐近非扩展映象的修正的迭代格式的强收敛定理.所得结果改进了Schu,Rhoades以及其他作者相关的结果.
Tensor products of commutative Banach algebras
U. B. Tewari
1982-01-01
Full Text Available Let A1, A2 be commutative semisimple Banach algebras and A1⊗∂A2 be their projective tensor product. We prove that, if A1⊗∂A2 is a group algebra (measure algebra of a locally compact abelian group, then so are A1 and A2. As a consequence, we prove that, if G is a locally compact abelian group and A is a comutative semi-simple Banach algebra, then the Banach algebra L1(G,A of A-valued Bochner integrable functions on G is a group algebra if and only if A is a group algebra. Furthermore, if A has the Radon-Nikodym property, then the Banach algebra M(G,A of A-valued regular Borel measures of bounded variation on G is a measure algebra only if A is a measure algebra.
A Characterization of Homomorphisms Between Banach Algebras
Jian Lian CUI; Jin Chuan HOU
2004-01-01
We show that every unital invertibility preserving linear map from avon Neumann algebra onto a semi-simple Banach algebra is a Jordan homomorphism; this gives an affirmative answer to a problem of Kaplansky for all yon Neumann algebras. For a unital linear map φ from a semi-simple complex Banach algebra onto another, we also show that the following statements are equivalent: (1)φ is an homomorphism; (2) φ is completely invertibility preserving; (3) φ is 2-invertibility preserving.
王娴; 何震
2004-01-01
Xu和Norr已经证明了建立在一致凸Banach空间的一个非空有界闭凸子集上的渐进非扩张映射的三步迭代的收敛定理问题.引入(L-α)一致李普希兹的概念,然后在一些已有结果的基础上,证明一致凸Banach空间的紧子集上的(L-α)一致李普希兹渐进非扩张映射的三步迭代序列的收敛问题.这个结论是对Xu和Noor的相应结果的推广.%Xu and Noor had proved the theorem on convergence of three-step iterations for asymptotically nonexpansive mapping on nonempty closed, bounded, and convex subset of uniformly convex Banach space. Based on some results given by K Tan and H K Xu[1] proved, the convergence of three-step iterations of (L-α) uniformly Lipschitz asymptotically nonexpansive mapping on a compact subset of a uniform convex Banach space had proved. The results presented extended the corresponding of Xu and Noor[5].
The Reflexive Adaptations of School Principals in a "Local" South African Space
Fataar, Aslam
2009-01-01
This paper is an analysis of the work of three principals in an impoverished black township in post-apartheid South Africa. Based on qualitative approaches, it discusses the principals' entry into the township, and their navigation of their schools' surrounding social dynamics. It combines the lenses of "space" and "performance" to analyse the…
Eventually and asymptotically positive semigroups on Banach lattices
Daners, Daniel; Glück, Jochen; Kennedy, James B.
2016-09-01
We develop a theory of eventually positive C0-semigroups on Banach lattices, that is, of semigroups for which, for every positive initial value, the solution of the corresponding Cauchy problem becomes positive for large times. We give characterisations of such semigroups by means of spectral and resolvent properties of the corresponding generators, complementing existing results on spaces of continuous functions. This enables us to treat a range of new examples including the square of the Laplacian with Dirichlet boundary conditions, the bi-Laplacian on Lp-spaces, the Dirichlet-to-Neumann operator on L2 and the Laplacian with non-local boundary conditions on L2 within the one unified theory. We also introduce and analyse a weaker notion of eventual positivity which we call "asymptotic positivity", where trajectories associated with positive initial data converge to the positive cone in the Banach lattice as t → ∞. This allows us to discuss further examples which do not fall within the above-mentioned framework, among them a network flow with non-positive mass transition and a certain delay differential equation.
on nonconvex sets in UCED Banach spaces
Wei-Shih Du
2002-01-01
direction. Furthermore, if {T i}i∈I is any compatible family of strongly nonexpansive self-mappings on such a C and the graphs of T i, i\t∈I, have a nonempty intersection, then T i, i∈I, have a common fixed point in C.
The Maslov index in symplectic Banach spaces
Booss-Bavnbek, Bernhelm; Zhu, Chaofeng
index. As an application, we consider curves of elliptic operators which have varying principal symbol, varying maximal domain and are not necessarily of Dirac type. For this class of operator curves, we derive a desuspension spectral ow formula for varying well-posed boundary conditions on manifolds...... such decompositions we dene the Maslov index of the curve by symplectic reduction to the classical nite-dimensional case. We prove the transitivity of repeated symplectic reductions and obtain the invariance of the Maslov index under symplectic reduction, while recovering all the standard properties of the Maslov...
Admissibility of Linear Systems in Banach Spaces
GUO Fa-ming
2005-01-01
In this paper, infinite-time p-admissibility of unbounded operators is introduced and the Co-semigroup characterization of the infinite-time p-admissibility of unbounded observation operators is given. Moreover, the analogous result for the infinite-time p-admissibility of unbounded control operators is presented.
Spectral theory of linear operators and spectral systems in Banach algebras
Müller, Vladimir
2003-01-01
This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. The theory is presented in a unified, axiomatic and elementary way. Many results appear here for the first time in a monograph. The material is self-contained. Only a basic knowledge of functional analysis, topology, and complex analysis is assumed. The monograph should appeal both to students who would like to learn about spectral theory and to experts in the field. It can also serve as a reference book. The present second edition contains a number of new results, in particular, concerning orbits and their relations to the invariant subspace problem. This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach alg...
On Riccati equations in Banach algebras
Curtain, Ruth F
2010-01-01
Let $R$ be a commutative complex Banach algebra with the involution $\\cdot ^\\star$ and suppose that $A\\in R^{n\\times n}$, $B\\in R^{n\\times m}$, $C\\in R^{p\\times n}$. The question of when the Riccati equation
(2-1)-Ideal amenability of triangular banach algebras
S Etemad; M Ettefagh
2015-05-01
Let $\\mathcal{A}$ and $\\mathcal{B}$ be two unital Banach algebras and let $\\mathcal{M}$ be an unital Banach $\\mathcal{A}$, $\\mathcal{B}$-module. Also, let $\\mathcal{T}=\\left[\\begin{smallmatrix} \\mathcal{A} & \\mathcal{M}\\\\ & \\mathcal{B}\\end{smallmatrix}\\right]$ be the corresponding triangular Banach algebra. Forrest and Marcoux (Trans. Amer. Math. Soc. 354 (2002) 1435–1452) have studied the -weak amenability of triangular Banach algebras. In this paper, we investigate (2-1)-ideal amenability of $\\mathcal{T}$ for all ≥ 1. We introduce the structure of ideals of these Banach algebras and then, we show that (2-1)-ideal amenability of $\\mathcal{T}$ depends on (2-1)-ideal amenability of Banach algebras $\\mathcal{A}$ and $\\mathcal{B}$.
Reid, Hazel; West, Linden
2016-01-01
This paper explores the constraints to innovative, creative and reflexive careers counselling in an uncertain neo-liberal world. We draw on previously reported research into practitioners' use of a narrative model for career counselling interviews in England and a Europe-wide auto/biographical narrative study of non-traditional learners in…
Reflexive Aero Structures for Enhanced Survivability Project
National Aeronautics and Space Administration — Cornerstone Research Group Inc. (CRG) will develop an advanced reflexive structure technology system to increase the survivability of future systems constructed of...
Hereditary properties of Amenability modulo an ideal of Banach algebras
Hamidreza Rahimi
2014-10-01
Full Text Available In this paper we investigate some hereditary properties of amenability modulo an ideal of Banach algebras. We show thatif $(e_{\\alpha}_{\\alpha}$ is a bounded approximate identity modulo $I$ of a Banach algebra $A$ and $X$ is a neo-unital modulo $I$, then $(e_{\\alpha}_{\\alpha}$ is a bounded approximate identity for $X$. Moreover we show that amenability modulo an ideal of a Banach algebra $A$ can be only considered by the neo-unital modulo $I$ Banach algebra over $A$
胡去非; 闫守峰
2008-01-01
将Banach-Steinhaus定理推广到拓扑向量空间上.设X,Y为拓扑向量空间,X是第二纲的.若A(∈)B0逐点有界,则A是等度连续的.B0表示X到Y的连续线性算子组成的向量空间.
Multipliers of Weighted Semigroups and Associated Beurling Banach Algebras
S J Bhatt; P A Dabhi; H V Dedania
2011-11-01
Given a weighted discrete abelian semigroup $(S,)$, the semigroup $M_(S)$ of -bounded multipliers as well as the Rees quotient $M_(S)/S$ together with their respective weights $\\overline{}$ and $\\overline{}_q$ induced by are studied; for a large class of weights , the quotient $\\ell^1(M_(S),\\overline{})/\\ell^1(S,)$ is realized as a Beurling algebra on the quotient semigroup $M_(S)/S$; the Gel’fand spaces of these algebras are determined; and Banach algebra properties like semisimplicity, uniqueness of uniform norm and regularity of associated Beurling algebras on these semigroups are investigated. The involutive analogues of these are also considered. The results are exhibited in the context of several examples.
Sifat Aljabar Banach Komutatif dan Elemen Identitas pada Kelas D(K
Malahayati Malahayati
2013-11-01
Full Text Available The first Baire class of bounded functions on separable metric spaces K denoted by B1(k. One of the most important subclass of B1(k is D(K, by D(K is denoted the class of all functions on K which are differences of bounded semicontinuous functions. In this paper we proved that D(K is abelian Banach algebra and identity element
Chistyakov, VV
2005-01-01
It is shown that the space of functions of n real variables with finite total variation in the sense of Vitali, Hardy and Krause, defined on a rectangle I-a(b) C R-n, is a Banach algebra under the pointwise operations and Hildebrandt-Leonov's norm. This result generalizes the classical case of funct
Characterization of a Banach-Finsler manifold in terms of the algebras of smooth functions
Jaramillo, J A; Sanchez-Gonzalez, L
2011-01-01
In this note we give sufficient conditions to ensure that the weak Finsler structure of a complete $C^k$ Finsler manifold $M$ is determined by the normed algebra $C_b^k(M)$ of all real-valued, bounded and $C^k$ smooth functions with bounded derivative defined on $M$. As a consequence, we obtain: (i) the Finsler structure of a finite-dimensional and complete $C^k$ Finsler manifold $M$ is determined by the algebra $C_b^k(M)$; (ii) the weak Finsler structure of a separable and complete $C^k$ Finsler manifold $M$ modeled on a Banach space with a Lipschitz and $C^k$ smooth bump function is determined by the algebra $C^k_b(M)$; (iii) the weak Finsler structure of a $C^k$ uniformly bumpable and complete $C^k$ Finsler manifold $M$ modeled on a Weakly Compactly Generated (WCG) Banach space with an (equivalent) $C^k$ smooth norm is determined by the algebra $C^k_b(M)$; and (iii) the isometric structure of a WCG Banach space $X$ with an $C^1$ smooth bump function is determined by the algebra $C_b^1(X)$.
Very Smooth Points of Spaces of Operators
T S S R K Rao
2003-02-01
In this paper we study very smooth points of Banach spaces with special emphasis on spaces of operators. We show that when the space of compact operators is an -ideal in the space of bounded operators, a very smooth operator attains its norm at a unique vector (up to a constant multiple) and ( ) is a very smooth point of the range space. We show that if for every equivalent norm on a Banach space, the dual unit ball has a very smooth point then the space has the Radon–Nikodým property. We give an example of a smooth Banach space without any very smooth points.
Supersets for the spectrum of elements in extended Banach algebras
Morteza Seddighin
1989-01-01
Full Text Available If A is a Banach Algebra with or without an identity, A can be always extended to a Banach algebra A¯ with identity, where A¯ is simply the direct sum of A and C, the algebra of complex numbers. In this note we find supersets for the spectrum of elements of A¯.
无
2000-01-01
Applications of locally fine property for operators are further developed. Let E and F be Banach spaces and f: be C1 nonlinear map, where U (x0) is an open set containing point x0∈E. With the locally fine property for Frechet derivatives f′(x) and generalized rank theorem for f′(x), a local conjugacy theorem, i.e. a characteristic condition for f being conjugate to f′(x0) near x0,is proved. This theorem gives a complete answer to the local conjugacy problem. Consequently, several rank theorems in advanced calculus are established, including a theorem for C1 Fredholm map which has been so far unknown. Also with this property the concept of regular value is extended, which gives rise to a generalized principle for constructing Banach submanifolds.
马吉溥
2000-01-01
Applications of locally fine property for operators are further developed. Let E and F be Banach spaces and f: U( x0) E—→F be C1 nonlinear map, where U (x0) is an open set containing point x0∈ E. With the locally fine property for Frechet derivatives f’ (x) and generalized rank theorem for f ’( x), a local conjugacy theorem, i. e. a characteristic condition for f being conjugate to f (x0) near x0,is proved. This theorem gives a complete answer to the local conjugacy problem. Consequently, several rank theorems in advanced calculus are established, including a theorem for C1 Fredholm map which has been so far unknown. Also with this property the concept of regular value is extended, which gives rise to a generalized principle for constructing Banach submanifolds.
Diederichsen, Louise; Krogsgaard, Michael; Voigt, Michael
2002-01-01
Dynamic shoulder stability is dependent on muscular coordination and sensory inputs. In the shoulder, mechanoreceptors are found in the coracoacromial ligament, the rotator cuff tendons, the musculotendinous junctions of the rotator cuff and in the capsule. The number of receptors in the capsule...... is small compared to the number in the other shoulder structures. Proprioceptive information from numerous receptors in muscles and tendons is mediated via fast conducting nervefibers and probably contribute more to kinaestethic sensation than information from capsule and ligaments. Therefore it seems...... likely that the joint receptors have a more distinct role for the kinaestethic sense than muscle receptors. In cats a direct reflex from the afferents innervating the shoulder to the muscles around the shoulder has been presented. The reflex had an extremely short latency (2.7-3.1 ms). In man, a very...
Wood, S. J.; Clarke, A. H.; Rupert, A. H.; Harm, D. L.; Clement, G. R.
2009-01-01
Two joint ESA-NASA studies are examining changes in otolith-ocular reflexes and motion perception following short duration space flights, and the operational implications of post-flight tilt-translation ambiguity for manual control performance. Vibrotactile feedback of tilt orientation is also being evaluated as a countermeasure to improve performance during a closed-loop nulling task. METHODS. Data is currently being collected on astronaut subjects during 3 preflight sessions and during the first 8 days after Shuttle landings. Variable radius centrifugation is utilized to elicit otolith reflexes in the lateral plane without concordant roll canal cues. Unilateral centrifugation (400 deg/s, 3.5 cm radius) stimulates one otolith positioned off-axis while the opposite side is centered over the axis of rotation. During this paradigm, roll-tilt perception is measured using a subjective visual vertical task and ocular counter-rolling is obtained using binocular video-oculography. During a second paradigm (216 deg/s, radius), the effects of stimulus frequency (0.15 - 0.6 Hz) are examined on eye movements and motion perception. A closed-loop nulling task is also performed with and without vibrotactile display feedback of chair radial position. PRELIMINARY RESULTS. Data collection is currently ongoing. Results to date suggest there is a trend for perceived tilt and translation amplitudes to be increased at the low and medium frequencies on landing day compared to pre-flight. Manual control performance is improved with vibrotactile feedback. DISCUSSION. One result of this study will be to characterize the variability (gain, asymmetry) in both otolithocular responses and motion perception during variable radius centrifugation, and measure the time course of postflight recovery. This study will also address how adaptive changes in otolith-mediated reflexes correspond to one's ability to perform closed-loop nulling tasks following G-transitions, and whether manual control
Wood, S. J.; Clarke, A. H.; Rupert, A. H.; Harm, D. L.; Clement, G. R.
2009-01-01
Two joint ESA-NASA studies are examining changes in otolith-ocular reflexes and motion perception following short duration space flights, and the operational implications of post-flight tilt-translation ambiguity for manual control performance. Vibrotactile feedback of tilt orientation is also being evaluated as a countermeasure to improve performance during a closed-loop nulling task. METHODS. Data is currently being collected on astronaut subjects during 3 preflight sessions and during the first 8 days after Shuttle landings. Variable radius centrifugation is utilized to elicit otolith reflexes in the lateral plane without concordant roll canal cues. Unilateral centrifugation (400 deg/s, 3.5 cm radius) stimulates one otolith positioned off-axis while the opposite side is centered over the axis of rotation. During this paradigm, roll-tilt perception is measured using a subjective visual vertical task and ocular counter-rolling is obtained using binocular video-oculography. During a second paradigm (216 deg/s, perception. A closed-loop nulling task is also performed with and without vibrotactile display feedback of chair radial position. PRELIMINARY RESULTS. Data collection is currently ongoing. Results to date suggest there is a trend for perceived tilt and translation amplitudes to be increased at the low and medium frequencies on landing day compared to pre-flight. Manual control performance is improved with vibrotactile feedback. DISCUSSION. One result of this study will be to characterize the variability (gain, asymmetry) in both otolithocular responses and motion perception during variable radius centrifugation, and measure the time course of postflight recovery. This study will also address how adaptive changes in otolith-mediated reflexes correspond to one's ability to perform closed-loop nulling tasks following G-transitions, and whether manual control performance can be improved with vibrotactile feedback of orientation.
倪仁兴
2003-01-01
用不同于通常的方法建立了非自反实Banach空间中的扰动优化J-Sup问题适定性的两个一般性定理,所得的结果推广或发展了包括Edelstein,Asplund,Panada and Kapoor,Zhivkov,Fitzpatrick,Baranger和作者等人在内的许多相应的结果.
Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras
Hirasawa Go
2005-01-01
Full Text Available We prove that a Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra is a ring homomorphism. Using a signum effectively, we can give a simple proof of the Hyers-Ulam-Rassias stability of a Jordan homomorphism between Banach algebras. As a direct corollary, we show that to each approximate Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra there corresponds a unique ring homomorphism near to .
三角Banach代数的等距同构%ISOMETRIC ISOMORPHISMS OF TRIANGULAR BANACH ALGEBRAS
骆建文; 陆芳言
2000-01-01
Let (X) and (X) be Banach algebras.Let (X) be a Banach (X),(X)-module with bounded 1.Then (X) is a Banach algebra with the usual operations and the norm ‖［AOMB］‖=‖A‖+‖M‖+‖B‖.Such an algebra is called a triangular Banach algebra.In this paper the isometric isomorphisms of triangular Banach algebras are characterized.
Mean ergodic operators and reflexive Fréchet lattices
Bonet, J.; De Pagter, B.; Ricker, W.J.
2011-01-01
Connections between (positive) mean ergodic operators acting in Banach lattices and properties of the underlying lattice itself are well understood (see the works of Emel'yanov, Wolff and Zaharopol). For Fréchet lattices (or more general locally convex solid Riesz spaces) there is virtually no infor
Lackner, J. R.; Graybiel, A.
1981-01-01
Recordings of horizontal nystagmus were obtained on 16 male subjects exposed to repeated patterns of horizontal angular acceleration, constant velocity rotation, and sudden-stop deceleration in the laboratory and in the free-fall and high-force periods of parabolic flight. Nystagmus intensity was a clear function of gravitoinertial force level: slow phase velocity and beat frequency increased during exposure to high force levels and decreased in free-fall compared to values obtained at 1 G. These findings indicate that the gain of the vestibulo-ocular reflex decreases in free-fall. This fact likely accounts for the disorientation and dizziness sometimes experienced by astronauts when moving their heads in the early phases of orbital flight and again after splashdown. The implications of the present findings, both for the etiology and for the treatment of space motion sickness, are discussed.
向雪萍; 孟京华; 李红
2011-01-01
对具数列的渐近非扩张型映像T给出了修正的Ishikawa Reich-Takahashi迭代序列,讨论其对T的不动点的强收敛性.同时,给出了T有不动点且序列Sm(y)=(1-αm)x+αm Tm y强收敛到T的不动点的充分条件,其中x∈D,y∈D,D是Banach空间E中闭凸子集,αm∈[0.1],αm→1.改进和推广了近期一些文献的相关结果.%The modified lshikawa Reich-Takahashi Iterative sequances for asymptotically nonexpansive type mapping T with sequence of number were discussed, which had a strong convergence for the fixed point of T. The sufficient conditions of the existence of fixed point of T and some sequences Sm (y) = ( 1 - am ) x + am,Tmy converging to a fLxed point of T were derived, with D being an nonempty closed convex subset of a Banach space E,x,y ∈ D, am, ∈[ 0,1 ] and am→l. The outcome improved and extended some recent results.
WEAKLY ALGEBRAIC REFLEXIVITY AND STRONGLY ALGEBRAIC REFLEXIVITY
TaoChangli; LuShijie; ChenPeixin
2002-01-01
Algebraic reflexivity introduced by Hadwin is related to linear interpolation. In this paper, the concepts of weakly algebraic reflexivity and strongly algebraic reflexivity which are also related to linear interpolation are introduced. Some properties of them are obtained and some relations between them revealed.
The Banach-Tarski paradox for flag manifolds
Komori, Yohei
2011-01-01
The famous Banach-Tarski paradox claims that the three dimensional rotation group acts on the two dimensional sphere paradoxically. In this paper, we generalize their result to show that the classical group acts on the flag manifold paradoxically.
Ideal Amenability of Banach Algebras on Locally Compact Groups
M Eshaghi Gordji; S A R Hosseiniun
2005-08-01
In this paper we study the ideal amenability of Banach algebras. Let $\\mathcal{A}$ be a Banach algebra and let be a closed two-sided ideal in $\\mathcal{A}, \\mathcal{A}$ is -weakly amenable if $H^1(\\mathcal{A},I^∗)=\\{0\\}$. Further, $\\mathcal{A}$ is ideally amenable if $\\mathcal{A}$ is -weakly amenable for every closed two-sided ideal in $\\mathcal{A}$. We know that a continuous homomorphic image of an amenable Banach algebra is again amenable. We show that for ideal amenability the homomorphism property for suitable direct summands is true similar to weak amenability and we apply this result for ideal amenability of Banach algebras on locally compact groups.
白小净; 魏文展
2015-01-01
This paper introduces the concept of smoothness and uniform smoothness and discusses the relationship that strictly convex and smoothness ,uniformly convex and uniform smoothness be‐tween Z-spaces and B-Z-spaces ,and gives the inference equivalence in reflexive B -Z -spaces .At the same time ,it introduces the concept of weak convexity and (E) property ,resulting in the relevant theorer of weak convexity and (E) property .%引入了Z－空间中光滑性与一致光滑性的概念，讨论了在Z －空间及B －Z －空间中严格凸性与光滑性、一致凸性与一致光滑性之间的关系，并且给出了它们在自反的B－Z －空间下等价的若干结果：还引入了B －Z－空间上的弱凸性与（E ）性质的概念，得出了弱凸性及（E ）性质的相关定理。
关于Banach共轭算子和Hilbert共轭算子的讨论%Discussion on Banach conjugate operator and Hilbert conjugate operator
杨纪华; 李艳秋
2014-01-01
Banach conjugate operator and Hilbert conjugate operator are two very important concepts in functional analysis. Hilbert space is a special Banach space,but the conjugate operator in Hilbert space does not follow the definition of conjugate operator in Banach space,and thevast majority textbooks don′t explain the reasons for this definition.Described the reason why conjugate operator in Hilbert space does not follow the definition of conjugate operator in Banach space,and discussed the relationship between the two operators.%Banach共轭算子和Hilbert共轭算子是泛函分析中两个非常重要的概念．Hilbert 空间是特殊的Banach空间，但Hilbert空间上的共轭算子没有沿用Banach空间上共轭算子的定义，并且绝大数教材都没有说明这样定义的原因．阐述了Hilbert空间上的共轭算子没有沿用Banach空间上共轭算子定义的原因，并讨论Hilbert空间中这两种算子的关系.
Amenability and Contractibility Modulo an Ideal of Banach Algebras
Hamidreza Rahimi
2014-01-01
Full Text Available We investigate the concept of amenability modulo an ideal of Banach algebra, showing that amenability modulo an ideal can be characterized by the existence of virtual and approximate diagonal modulo an ideal. We also study the concept of contractible modulo an ideal of Banach algebra. As a consequence, we prove a version of Selivanov's theorem for a large class of semigroups, including E-inversive E-semigroup and eventually inverse semigroups.
Co cycle Perturbation on Banach Algebras
Shi Luo-yi; Wu Yu-jing
2014-01-01
Letαbe a flow on a Banach algebra B, and t 7→ut a continuous function from R into the group of invertible elements of B such that usαs(ut)=us+t, s, t∈R. Then βt =Adut◦αt, t∈R is also a flow on B, where Adut(B) , utBu-1t for any B ∈ B. β is said to be a cocycle perturbation of α. We show that if α, β are two flows on a nest algebra (or quasi-triangular algebra), thenβ is a cocycle perturbation ofα. And the flows on a nest algebra (or quasi-triangular algebra) are all uniformly continuous.
Bojana Mihailović; Marija Rašajski; Zoran Stanić
2016-01-01
A graph is called reflexive if its second largest eigenvalue does not exceed 2. We survey the results on reflexive cacti obtained in the last two decades. We also discuss various patterns of appearing of Smith graphs as subgraphs of reflexive cacti. In the Appendix, we survey the recent results concerning reflexive bipartite regular graphs.
Baxandall, M L; Thorn, J L
1988-06-01
The oculocardiac reflex is well described and recognised in anaesthesia. The nasocardiac reflex is less well-known. We describe a clinical manifestation of this reflex and describe the relevant anatomy. This reflex may be obtunded during general anaesthesia. during general anaesthesia.
Reflexives in Veracruz Huastec.
Constable, Peter G.
A study examines various Huastec clause types that are reflexive in some sense, including ordinary reflexives, which involve co-reference. Two mutually exclusive morphosyntactic devices are used in Huastec: reflexive pronouns and verbal morphology. In this way, Huastec is like various European languages. Clauses involving reflexive pronouns and…
Stability of -Jordan Homomorphisms from a Normed Algebra to a Banach Algebra
Yang-Hi Lee
2013-01-01
Full Text Available We establish the hyperstability of -Jordan homomorphisms from a normed algebra to a Banach algebra, and also we show that an -Jordan homomorphism between two commutative Banach algebras is an -ring homomorphism.
B-valued martingale spaces with small index and atomic decompositions
刘培德; 于林
2001-01-01
Some atomic decomposition theorems for Banach-space-valued martingales are established. Using them, the embedding relationships between martingale spaces with small index are discussed. The results obtained here are connected closely with the p-uniform smoothness and q-uniform convexity of Banach space in which the martingales take values.
Atomic Decompositions of Weak Hardy Spaces of B-Valued Martingales
MA Tao; LIU Peide
2006-01-01
The atomic decompositions of weak Hardy spaces of Banach-space-valued martingales are given. With the help of the atomic decompositions, some inequalities for B-valued martingales are established in the case 0 ＜ r≤ 1.Here the results are connected closely with the p-uniform smoothness and q-uniform convexity of Banach spaces which the martingales take values in.
M. Kanani Arpatapeh∗
2015-12-01
Full Text Available Let A and B be unital Banach algebras and M be a left A-module and right B-module. We consider generalized derivations associate with Hochschild 2-cocycles on triangular Banach algebra T (related to A, B and M. We characterize this new version of generalized derivations on triangular Banach algebras and we obtain some results for l 1 − direct summands of Banach algebras
Convexity and Banach-Saks Property%凸性和Banach-Saks性质
方习年; 王建华
2002-01-01
该文引入ω-NUC空间、(k,k+l)-UR空间,证明了:ω-NUC空间具有Banach-Saks性质(B.S.P),从而推广了[1]中的结果,且包含[2]中相应的结果;2)严格凸的ω-NUC空间是ωR空间;3)k-UR空间是(k,k+l)-UR空间,(k,k+l)-UR空间是(k+l)-NUC空间,这个结论改进和包含了文[2]中的一个结果.
Uniqueness of the maximal ideal of the Banach algebra of bounded operators on $C([0,\\omega_1])$
Kania, Tomasz
2011-01-01
Let $\\omega_1$ be the first uncountable ordinal. By a result of Rudin, bounded operators on the Banach space $C([0,\\omega_1])$ have a natural representation as $[0,\\omega_1]\\times 0,\\omega_1]$-matrices. Loy and Willis observed that the set of operators whose final column is continuous when viewed as a scalar-valued function on $[0,\\omega_1]$ defines a maximal ideal of codimension one in the Banach algebra $\\mathscr{B}(C([0,\\omega_1]))$ of bounded operators on $C([0,\\omega_1])$. We give a coordinate-free characterization of this ideal and deduce from it that $\\mathscr{B}(C([0,\\omega_1]))$ contains no other maximal ideals. We then obtain a list of equivalent conditions describing the strictly smaller ideal of operators with separable range, and finally we investigate the structure of the lattice of all closed ideals of $\\mathscr{B}(C([0,\\omega_1]))$.
Pagis, Michal
2009-01-01
Drawing on G. H. Mead and Merleau-Ponty, this paper aims to extend our understanding of self-reflexivity beyond the notion of a discursive, abstract, and symbolic process. It offers a framework for embodied self-reflexivity, which anchors the self in the reflexive capacity of bodily sensations. The data consist of two years of ethnographic…
Almost Lie structures on an anchored Banach bundle
Cabau, Patrick
2011-01-01
Under appropriate assumptions, we generalize the concept of linear almost Poisson struc- tures, almost Lie algebroids, almost differentials in the framework of Banach anchored bundles and the relation between these objects. We then obtain an adapted formalism for mechanical systems which is illustrated by the evolutionary problem of the "Hilbert snake"
Approximate Preservers on Banach Algebras and C*-Algebras
M. Burgos
2013-01-01
Full Text Available The aim of the present paper is to give approximate versions of Hua’s theorem and other related results for Banach algebras and C*-algebras. We also study linear maps approximately preserving the conorm between unital C*-algebras.
Di Girolami, Cristina
2011-01-01
This paper concerns a class of Banach valued processes which have finite quadratic variation. The notion introduced here generalizes the classical one, of M\\'etivier and Pellaumail which is quite restrictive. We make use of the notion of $\\chi$-covariation which is a generalized notion of covariation for processes with values in two Banach spaces $B_{1}$ and $B_{2}$. $\\chi$ refers to a suitable subspace of the dual of the projective tensor product of $B_{1}$ and $B_{2}$. We investigate some $C^{1}$ type transformations for various classes of stochastic processes admitting a $\\chi$-quadratic variation and related properties. If $\\X^1$ and $\\X^2$ admit a $\\chi$-covariation, $F^i: B_i \\rightarrow \\R$, $i = 1, 2$ are of class $C^1$ with some supplementary assumptions then the covariation of the real processes $F^1(\\X^1)$ and $F^2(\\X^2)$ exist. A detailed analysis will be devoted to the so-called window processes. Let $X$ be a real continuous process; the $C([-\\tau,0])$-valued process $X(\\cdot)$ defined by $X_t(y)...
Approximately Linear Mappings in Banach Modules over a C*-algebra
Choonkil PARK; Jian Lian CUI
2007-01-01
Let X and Y be vector spaces. The authors show that a mapping f: X → Y satisfies the functional equation 2df(∑2dj=1(-1)j+1xj/2d)=∑2dj=1(-1)j+1f(xj) with f(0) = 0 if and only if the mapping f: X → Y is Cauchy additive, and prove the stability of the functional equation (++) in Banach modules over a unital C*-algebra, and in Poisson Banach modules over a unital Poisson C*-algebra. Let A and B be unital C*-algebras, Poisson C*-algebras or Poisson JC*-algebras. As an application, the authors show that every almost homomorphism h: A → B of A into B is a homomorphism when h((2d-1)nuy) = h((2d-1)nu)h(y) or h((2d-1)nuoy) = h((2d-1)nu)oh(y) for all unitaries u ∈ A, all y ∈ A, n= 0, 1, 2,....Moreover, the authors prove the stability of homomorphisms in C*-algebras, Poisson C*-algebras or Poisson JC*-algebras.
The smooth Banach submanifold B*(E,F) in B(E,F)
无
2009-01-01
Let E,F be two Banach spaces,B(E,F),B+(E,F),Φ(E,F),SΦ(E,F) and R(E,F) be bounded linear,double splitting,Fredholm,semi-Frdholm and finite rank operators from E into F,respectively. Let Σ be any one of the following sets:{T ∈Φ(E,F):Index T=constant and dim N(T)=constant},{T ∈ SΦ(E,F):either dim N(T)=constant< ∞ or codim R(T)=constant< ∞} and {T ∈ R(E,F):Rank T=constant< ∞}. Then it is known that Σ is a smooth submanifold of B(E,F) with the tangent space TAΣ={B ∈ B(E,F):BN(A)-R(A) } for any A ∈Σ. However,for B*(E,F)={T ∈ B+(E,F):dimN(T)=codimR(T)= ∞} without the characteristic numbers,dimN(A) ,codimR(A) ,index(A) and Rank(A) of the equivalent classes above,it is very diffcult to find which class of operators in B*(E,E) forms a smooth submanifold of B(E,F) . Fortunately,we find that B*(E,F) is just a smooth submanifold of B(E,F) with the tangent space TAB*(E,F)={T ∈ B(E,F) :T N(A) -R(A) } for each A ∈ B*(E,F) . Thus the geometric construction of B+(E,F) is obtained,i.e.,B+(E,F) is a smooth Banach submanifold of B(E,F) ,which is the union of the previous smooth submanifolds disjoint from each other. Meanwhile we give a smooth submanifold S(A) of B(E,F) ,modeled on a fixed Banach space and containing A for any A ∈ B+(E,F) . To end these,results on the generalized inverse perturbation analysis are generalized. Specially,in the case E=F=Rn,it is obtained that the set Σr of all n × n matrices A with Rank(A)=r < n is an arcwise connected and smooth hypersurface(submanifold) in B(Rn) with dimΣr=2nr-r2. Then a new geometrical construction of B(Rn) ,analogous to B+(E,F) ,is given besides its analysis and algebra constructions known well.
Emotionally Colorful Reflexive Games
Tarasenko, Sergey
2011-01-01
This study addresses the matter of reflexive control of the emotional states by means of Reflexive Game Theory (RGT). It is shown how to build a bridge between RGT and emotions. For this purpose the Pleasure-Arousal-Dominance (PAD) model is adopted. The major advantages of RGT are its ability to predict human behavior and unfold the entire spectra of reflexion in the human mind. On the other hand, PAD provides ultimate approach to model emotions. It is illustrated that emotions are reflexive processes and, consequently, RGT fused with PAD model is natural solution to model emotional interactions between people. The fusion of RGT and PAD, called Emotional Reflexive Games (ERG), inherits the key features of both components. Using ERG, we show how reflexive control can be successfully applied to model human emotional states. Up to date, EGR is a unique methodology capable of modeling human reflexive processes and emotional aspects simultaneously.
The Fontana paradoxical reflex?
Lavorini, Federico; Fontana, Giovanni; Chellini, Elisa; Magni, Chiara; Pistolesi, Massimo; Widdicombe, John
2011-09-01
This commentary describes the "deflation cough" caused by deep lung deflations. Deflation cough is a paradoxical reflex similar to that described by Henry Head in 1889 for lung inflations that probably is mediated by the same sensors and afferent fibers in the lungs and activated by gastroesophageal reflux. We discuss how this reflex must be self-limiting, the general role of paradoxical reflexes in the body, and the possible clinical significance of deflation cough.
Krogsgaard, Michael R; Dyhre-Poulsen, Poul; Fischer-Rasmussen, Torsten
2002-01-01
The idea of muscular reflexes elicited from sensory nerves of the cruciate ligaments is more than 100 years old, but the existence of such reflexes has not been proven until the recent two decades. First in animal experiments, a muscular excitation could be elicited in the hamstrings when the ant...
The Quest for the Ultimate Anisotropic Banach Space
Baladi, Viviane
2017-02-01
We present a new scale U^{t,s}_p (s1 and -1+1/pMonograph, 2016; Baladi and Ruelle in Ergod Theory Dyn Syst 14:621-632, 1994; Baladi and Ruelle in Invent Math 123:553-574, 1996) to study dynamical determinants and zeta functions.
Fixed points of holomorphic mappings for domains in Banach spaces
Lawrence A. Harris
2003-01-01
Full Text Available We discuss the Earle-Hamilton fixed-point theorem and show how it can be applied when restrictions are known on the numerical range of a holomorphic function. In particular, we extend the Earle-Hamilton theorem to holomorphic functions with numerical range having real part strictly less than 1. We also extend the Lumer-Phillips theorem estimating resolvents to dissipative holomorphic functions.
On some fixed point theorems in Banach spaces
D. V. Pai
1982-01-01
Full Text Available In this paper, some fixed point theorems are proved for multi-mappings as well as a pair of mappings. These extend certain known results due to Kirk, Browder, Kanna, Ćirić and Rhoades.
Tools for analysis of Dirac structures on banach spaces
Iftime, Orest V.; Sandovici, Adrian; Golo, Goran
2005-01-01
Power-conserving and Dirac structures are known as an approach to mathematical modeling of physical engineering systems. In this paper connections between Dirac structures and well known tools from standard functional analysis are presented. The analysis can be seen as a possible starting framework
Stochastic antiderivational equations on non-Archimedean Banach spaces
S. V. Ludkovsky
2003-01-01
non-Archimedean fields are investigated. Theorems about existence and uniqueness of the solutions are proved under definite conditions. In particular, Wiener processes are considered in relation to the non-Archimedean analog of the Gaussian measure.
The Socle and Finite Dimensionality of some Banach Algebras
Ali Ghaffari; Ali Reza Medghalchi
2005-08-01
The purpose of this note is to describe some algebraic conditions on a Banach algebra which force it to be finite dimensional. One of the main results in Theorem 2 which states that for a locally compact group , is compact if there exists a measure in $\\mathrm{Soc} (L^1(G))$ such that () ≠ 0. We also prove that is finite if $\\mathrm{Soc}(M(G))$ is closed and every nonzero left ideal in () contains a minimal left ideal.
Sobre la diferenciabilidad de funciones en espacios de Banach
Roberto C. Cabrales
2006-01-01
Full Text Available Se da un criterio que establece la diferenciabilidad de una función f : X → Y , donde X y Y son espacios de Banach. Este criterio se aplica además para obtener las reglas usuales del cálculo diferencial de una forma elemental, y también para obtener la diferenciabilidad de algunas normas de espacios funcionales clásicos.
de Jeu, Marcel
2012-01-01
If X is a compact Hausdorff space, supplied with a homeomorphism, then a crossed product involutive Banach algebra is naturally associated with these data. If X consists of one point, then this algebra is the group algebra of the integers. In this paper, we study spectral synthesis for the closed ideals of this associated algebra in two versions, one modeled after C(X), and one modeled after the group algebra of the integers. We identify the closed ideals which are equal to (what is the analogue of) the kernel of their hull, and determine when this holds for all closed ideals, i.e., when spectral synthesis holds. In both models, this is the case precisely when the homeomorphism has no periodic points.
Lectures given at the Banach Center and C.I.M.E. Joint Summer School
Lachowicz, Mirosław
2008-01-01
The aim of this volume that presents Lectures given at a joint CIME and Banach Center Summer School, is to offer a broad presentation of a class of updated methods providing a mathematical framework for the development of a hierarchy of models of complex systems in the natural sciences, with a special attention to Biology and Medicine. Mastering complexity implies sharing different tools requiring much higher level of communication between different mathematical and scientific schools, for solving classes of problems of the same nature. Today more than ever, one of the most important challenges derives from the need to bridge parts of a system evolving at different time and space scales, especially with respect to computational affordability. As a result the content has a rather general character; the main role is played by stochastic processes, positive semigroups, asymptotic analysis, kinetic theory, continuum theory and game theory.
Mario Cardano
2014-01-01
Full Text Available This essay deals with a relevant and controversial topic – objectivity in ethnographic research. More specifically, I would like to examine how reflexive procedures, more precisely “reflexive account”, can increase the robustness of results gained through an ethnographic research. The essay is organized in five parts. I will start by giving a preliminary definition of the two key concepts which are at the center of the analysis – objectivity and reflexivity. I will then give a brief description of the epistemological framework in which the proposed conceptions of objectivity and reflexivity are located. Thirdly, I move on to consider the epistemic status of ethnographic research, and will emphasize that ethnographies are not just “theory-laden”, as many writers have stated, but also “praxis” or “procedure laden”. In other words, I will stress that it is not only theories which are inevitably embedded in research, influencing how observations can be made; much the same can also be said of the concrete research practices which contribute to determine the experience of the ethnographer and its representation in a text. Fourthly, I will discuss why it is useful to employ reflexive practices, and then immediately afterwards will illustrate the ways in which reflexive descriptions can contribute to greater objectivity of ethnographic accounts. In conclusion, I will discuss a number of objections which have been raised against this use of reflexivity.
[Value of blink reflex studies in neurosurgical problems].
Jamjoom, Z; Nahser, H C; Nau, H E
1983-09-01
Blinking reflex studies were done in neurosurgical patients with processes in the posterior fossa and idiopathic trigeminal neuralgia. Alterations were found in space occupying, ischemic, and traumatic lesions of the trigemino-facial system. The analysis of the components of the blinking reflex can give hints to the site of the lesion and also to the prognosis of the underlying process.
SMOOTH AND PATH CONNECTED BANACH SUBMANIFOLD ∑r OF B(E,F) AND A DIMENSION FORMULA IN B(IRn,IRm)
Jipu Ma
2008-01-01
Given two Banach spaces E, F, let B(E, F) be the set of all bounded linear oper-ators from E into F, ∑r the set of all operators of finite rank r in B(E, F), and ∑#r the number of path connected components of ∑r. It is known that ∑r is a smooth Banach submani-fold in B(E, F) with given expression of its tangent space at each A ∈∑r. In this paper, the equality ∑#r = 1 is proved. Consequently, the following theorem is obtained: for any non-negative integer r, ∑r is a smooth and path connected Banach submanifold in B(E, F) with the tangent space TA∑r={B∈B(E,F): BN(A) R(A)} at each A∈∑r if dim F = ∞. Note that the routine method can hardly be applied here. So in addition to the nice topological and geometric property of ∑r the method presented in this paper is also interesting. As an application of this result, it is proved that if E = IRn and F = IRm, then ∑r is a smooth and path connected submanifold of B(IRn,IRm) and its dimension is dim ∑r = (m + n)r- r2 for each r, 0 ≤ r < min{n,m}.
Banach 格上的b-AM-紧算子%b-AM-compact Operators on Banach Lattices
程娜; 陈滋利
2010-01-01
本文对Banach 格上的b-AM-紧算子进行了描述,得到了如下三个结论:1) 如果Banach 格F 是无限维的,则E 是KB-空间当且仅当每个从E 到F 的AM-紧算子是b-AM-紧算子.2) Banach 格E 是离散的KB-空间当且仅当每个从E 到F 的连续算子是b-AM-紧算子.3) 如果E' 是离散的,则每个从E 到F 的b-弱紧算子是b-AM-紧算子.其次给出了b-AM-紧算子的控制性质,得到如下两个结论:1) 如果E 和F 是两个Banach 格,算子S,T : E →F 满足0≤S≤T 且T 是b-AM-紧算子,则算子S 是b-AM-紧算子当且仅当F 具有序连续范数或者E' 是离散空间.2) 如果S; T 是从E 到F 的算子满足0 ≤S ≤T,如果T 是b-AM-紧算子,则S2 也是b-AM-紧算子.
Petrov, S.
2000-08-20
An information system is reflexive if it stores a description of its current structure in the body of stored information and is acting on the base of this information. A data model is reflexive, if its language is meta-closed and can be used to build such a system. The need for reflexive data models in new areas of information technology applications is argued. An attempt to express basic notions related to information systems is made in the case when the system supports and uses meta-closed representation of the data.
A RANK THEOREM FOR NONLINEAR SEMI-FREDHOLM OPERATORS BETWEEN TWO BANACH MANIFOLDS
无
2006-01-01
In this article the concept of local conjugation of a C1 mapping between two Banach manifolds is introduced. Then a rank theorem for nonlinear semi-Fredholm operators between two Banach manifolds and a finite rank theorem are established in global analysis.
Integración en espacios de Banach
Rodríguez Ruiz, José
2006-01-01
Esta tesis doctoral se enmarca dentro de la teoría de integración de funciones con valores en espacios de Banach. Analizamos con detalle la integral de Birkhoff de funciones vectoriales, así como sus correspondientes versiones dentro de los contextos de la integración respecto de medidas vectoriales y la integración de multi-funciones. Comparamos estos métodos de integración con otros bien conocidos (integrales de Bochner, Pettis, McShane, Debreu, etc.). Caracterizamos, en términos de integra...
Using ESO Reflex with Web Services
Järveläinen, P.; Savolainen, V.; Oittinen, T.; Maisala, S.; Ullgrén, M. Hook, R.
2008-08-01
ESO Reflex is a prototype graphical workflow system, based on Taverna, and primarily intended to be a flexible way of running ESO data reduction recipes along with other legacy applications and user-written tools. ESO Reflex can also readily use the Taverna Web Services features that are based on the Apache Axis SOAP implementation. Taverna is a general purpose Web Service client, and requires no programming to use such services. However, Taverna also has some restrictions: for example, no numerical types such integers. In addition the preferred binding style is document/literal wrapped, but most astronomical services publish the Axis default WSDL using RPC/encoded style. Despite these minor limitations we have created simple but very promising test VO workflow using the Sesame name resolver service at CDS Strasbourg, the Hubble SIAP server at the Multi-Mission Archive at Space Telescope (MAST) and the WESIX image cataloging and catalogue cross-referencing service at the University of Pittsburgh. ESO Reflex can also pass files and URIs via the PLASTIC protocol to visualisation tools and has its own viewer for VOTables. We picked these three Web Services to try to set up a realistic and useful ESO Reflex workflow. They also demonstrate ESO Reflex abilities to use many kind of Web Services because each of them requires a different interface. We describe each of these services in turn and comment on how it was used
CHENG LIXIN; TENG YANMEI
2005-01-01
This paper presents a type of variational principles for real valued w* lower semicon tinuous functions on certain subsets in duals of locally convex spaces, and resolve a problem concerning differentiability of convex functions on general Banach spaces. They are done through discussing differentiability of convex functions on nonlinear topological spaces and convexification of nonconvex functions on topological linear spaces.
Corneomandibular reflex: Anatomical basis
Michele Pistacchi
2015-01-01
Full Text Available Corneomandibular reflex is a pathological phenomenon evident in cases of severe brainstem damage. It is considered to be a pathological exteroceptive reflex, associated with precentro bulbar tract lesions. The sign is useful in distinguishing central neurological injuries to metabolic disorders in acutely comatose patients, localizing lesions to the upper brainstem area, determining the depth of coma and its evolution, providing evidence of uncal or transtentorial herniation in acute cerebral hemisphere lesions, and it is a marker of supraspinal level impairment in amyotrophic lateral sclerosis and multiple sclerosis. This sign was evident in a patient with severe brain damage. We discuss the literature findings and its relevance in prognosis establishment.
Geometry of Müntz spaces and related questions
Gurariy, Vladimir
2005-01-01
Starting point and motivation for this volume is the classical Muentz theorem which states that the space of all polynomials on the unit interval, whose exponents have too many gaps, is no longer dense in the space of all continuous functions. The resulting spaces of Muentz polynomials are largely unexplored as far as the Banach space geometry is concerned and deserve the attention that the authors arouse. They present the known theorems and prove new results concerning, for example, the isomorphic and isometric classification and the existence of bases in these spaces. Moreover they state many open problems. Although the viewpoint is that of the geometry of Banach spaces they only assume that the reader is familiar with basic functional analysis. In the first part of the book the Banach spaces notions are systematically introduced and are later on applied for Muentz spaces. They include the opening and inclination of subspaces, bases and bounded approximation properties and versions of universality.
Vector Spaces of Non-measurable Functions
Francisco J. GARC(I)A-PACHECO; Juan B. SEOANE-SEP(U)LVEDA
2006-01-01
We show that there exists an infinite dimensional vector space every non-zero element of which is a non-measurable function. Moreover, this vector space can be chosen to be closed and to have dimensionβ for any cardinalityβ. Some techniques involving measure theory and density characters of Banach spaces are used.
Identification of Spinal Reflexes
De Vlugt, E.
2004-01-01
Visco-elasticity of joints is important for the maintenance of the human body posture and can in two manners be regulated. By means of cocontraction of antagonistic muscle groups and by neural reflexive feedback of muscle length and muscle strength, measured both by means of sensors in the muscles.
van Gijn, J
1995-11-01
The plantar response is a reflex that involves not only the toes, but all muscles that shorten the leg. In the newborn the synergy is brisk, involving all flexor muscles of the leg; these include the toe 'extensors', which also shorten the leg on contraction and therefore are flexors in a physiological sense. As the nervous system matures and the pyramidal tract gains more control over spinal motoneurones the flexion synergy becomes less brisk, and the toe 'extensors' are no longer part of it. The toes then often go down instead of up, as a result of a segmental reflex involving the small foot muscles and the overlying skin, comparable to the abdominal reflexes. With lesions of the pyramidal system, structural or functional, this segmental, downward response of the toes disappears, the flexion synergy may become disinhibited and the extensor hallucis longus muscle is again recruited into the flexion reflex of the leg: the sign of Babinski. A true Babinski sign denotes dysfunction of the pyramidal tract, and should be clearly distinguished from upgoing toes that do not belong to the flexion synergy of the leg. Correct interpretation of the plantar response depends only to a minor degree on the method or site of stimulation of the foot. It is therefore most important to assess the response in the entire leg.
Remark on Regularity of Continuous Operators on AL-Spaces
冯勋省; 陈滋利
2004-01-01
Let E and F be Banach lattices. It is known that if every continuous linear operator from E into F is regular, then, under some mild assumptions on E or F, either E is lattice isomorphic to an AL-space or F is lattice isomorphic to an AM-space. Here we present a characterization on an AL-space E such that every bounded linear operator from E into a Banach lattice is regular. A counterexample is also provided, which shows that the results are unexpected even if the domain is an AL-space or the range space is an AM-space.
Three classes of smooth Banach submanifolds in B(E,F)
Ji-pu Ma
2007-01-01
Let E, F be two Banach spaces, and B(E, F), Φ(E, F), SΦ(E, F) and R(E,F) be the bounded linear, Fredholm, semi-Frdholm and finite rank operators from E into F, respectively. In this paper, using the continuity characteristics of generalized inverses of operators under small perturbations, we prove the following result: Let ∑ be any one of the following sets: {T ∈ Φ(E, F): IndexT =const, and dim N(T) = const.}, {T ∈ SΦ(E, F): either dim N(T) = const. ＜ ∞ or codim R(T) = const.＜ ∞} and {T ∈ R(E, F): RankT =const.＜∞}. Then ∑ is a smooth submanifold of B(E, F) with the tangent space TA∑ = {B ∈ B(E,F): BN(A) (∪) R(A)} for any A ∈ ∑. The result is available for the further application to Thom's famous results on the transversility and the study of the infinite dimensional geometry.
Bapurao C. Dhage
2006-03-01
Full Text Available In this paper, we prove an existence theorem for hyperbolic differential equations in Banach algebras under Lipschitz and Caratheodory conditions. The existence of extremal solutions is also proved under certain monotonicity conditions.
Inequalities of Čebyšev Type for Lipschitzian Functions in Banach Algebras
Boldea Marius V.
2016-12-01
Full Text Available In this paper we give some Čebyšev type norm inequalities for two Lipschitzian functions on Banach algebras. Some examples for power function, exponential and the resolvent functions are also provided
Spinal reflexes in brain death.
Beckmann, Yesim; Çiftçi, Yeliz; Incesu, Tülay Kurt; Seçil, Yaprak; Akhan, Galip
2014-12-01
Spontaneous and reflex movements have been described in brain death and these unusual movements might cause uncertainties in diagnosis. In this study we evaluated the presence of spinal reflexes in patients who fulfilled the criteria for brain death. Thirty-two (22 %) of 144 patients presented unexpected motor movements spontaneously or during examinations. These patients exhibited the following signs: undulating toe, increased deep tendon reflexes, plantar responses, Lazarus sign, flexion-withdrawal reflex, facial myokymia, neck-arm flexion, finger jerks and fasciculations. In comparison, there were no significant differences in age, sex, etiology of brain death and hemodynamic laboratory findings in patients with and without reflex motor movement. Spinal reflexes should be well recognized by physicians and it should be born in mind that brain death can be determined in the presence of spinal reflexes.
-Metric Space: A Generalization
Farshid Khojasteh
2013-01-01
Full Text Available We introduce the notion of -metric as a generalization of a metric by replacing the triangle inequality with a more generalized inequality. We investigate the topology of the spaces induced by a -metric and present some essential properties of it. Further, we give characterization of well-known fixed point theorems, such as the Banach and Caristi types in the context of such spaces.
Karim Nikkhah
2017-01-01
Full Text Available Interesting phenomena of reflex epileptic syndromes are characterized by epileptic seizures each one induced by specific stimulus with a variety of types. Simple triggers, which lead to seizures within seconds, are of sensory type (most commonly visual, most rarely tactile or proprioceptive stimuli. Complex triggers, which are mostly of cognitive type such as praxis, reading, talking, and music, usually induce the epileptic event within minutes. It should differ from what most epileptic patients report as provocative precipitants for seizures (such as emotional stress, fatigue, fever, sleep deprivation, alcohol, and menstrual cycle. The identification of a specific trigger is not only important for patients or their parents to avoid seizures, but also it might help neurologists to choose the most effective antiepileptic drug for each case. In addition, research in this area may possibly reveal some underlying pathophysiology of epileptic phenomena in the brain.In this review, we briefly introduce reported reflex epileptic seizures, their clinical features and management.
Spaces of continuous functions over Dugundji compacta
2006-01-01
We show that for every Dugundji compact $K$ of weight aleph one the Banach space $C(K)$ is 1-Plichko and the space $P(K)$ of probability measures on $K$ is Valdivia compact. Combining this result with the existence of a non-Valdivia compact group, we answer a question of Kalenda.
Perceptual rivalry: reflexes reveal the gradual nature of visual awareness.
Marnix Naber
Full Text Available Rivalry is a common tool to probe visual awareness: a constant physical stimulus evokes multiple, distinct perceptual interpretations ("percepts" that alternate over time. Percepts are typically described as mutually exclusive, suggesting that a discrete (all-or-none process underlies changes in visual awareness. Here we follow two strategies to address whether rivalry is an all-or-none process: first, we introduce two reflexes as objective measures of rivalry, pupil dilation and optokinetic nystagmus (OKN; second, we use a continuous input device (analog joystick to allow observers a gradual subjective report. We find that the "reflexes" reflect the percept rather than the physical stimulus. Both reflexes show a gradual dependence on the time relative to perceptual transitions. Similarly, observers' joystick deflections, which are highly correlated with the reflex measures, indicate gradual transitions. Physically simulating wave-like transitions between percepts suggest piece-meal rivalry (i.e., different regions of space belonging to distinct percepts as one possible explanation for the gradual transitions. Furthermore, the reflexes show that dominance durations depend on whether or not the percept is actively reported. In addition, reflexes respond to transitions with shorter latencies than the subjective report and show an abundance of short dominance durations. This failure to report fast changes in dominance may result from limited access of introspection to rivalry dynamics. In sum, reflexes reveal that rivalry is a gradual process, rivalry's dynamics is modulated by the required action (response mode, and that rapid transitions in perceptual dominance can slip away from awareness.
A Riesz representation theory for completely regular Hausdorff spaces and its applications
Nowak Marian
2016-01-01
Full Text Available Let X be a completely regular Hausdorff space, E and F be Banach spaces. Let Cb(X, E be the space of all E-valued bounded, continuous functions on X, equipped with the strict topology β. We develop the Riemman-Stieltjes-type Integral representation theory of (β, || · ||F -continuous operators T : Cb(X, E → F with respect to the representing Borel operator measures. For X being a k-space, we characterize strongly bounded (β, || · ||F-continuous operators T : Cb(X, E → F. As an application, we study (β, || · ||F-continuous weakly compact and unconditionally converging operators T : Cb(X, E → F. In particular, we establish the relationship between these operators and the corresponding Borel operator measures given by the Riesz representation theorem. We obtain that if X is a k-spaceand E is reflexive, then (Cb(X, E, β has the V property of Pełczynski.
Ratner, Helene
highlighted non-symmetric relationships between observer and observed and accused the academic text of enacting a realist genre, concealing the relativism entailed in textual production (Clifford and Marcus 1986, Woolgar 1988, Ashmore 1989). On the other hand, the reflexivity program produced fears...... of a “corrosive relativism in which everything is but a more or less clever expression of opinion” (Geertz 1988:2, 3) and it has suffered the little flattering accusations of piling "layer upon layer of self-consciousness to no avail" (Latour 1988:170) with little “interest [for] … theoretically ambitious...
Fixed Points of Non-expansive Operators on Weakly Cauchy Normed Spaces
Sahar M. Ali
2007-01-01
Full Text Available We proved the existence of fixed points of non-expansive operators defined on weakly Cauchy spaces in which parallelogram law holds, the given normed space is not necessarily be uniformly convex Banach space or Hilbert space, we reduced the completeness and the uniform convexity assumptions which imposed on the given normed space.
Stability results for generalized contractions in partial metric spaces
Fatma Al- Sirehy
2012-07-01
Full Text Available In 1994, Mathews [7] introduced the notion of partial metric spaces as a part of his study of denotational semantics of data.ow networks and obtained a generalization of the Banach contraction principle in partial metric spaces. In this paper, we prove stability results in partial metric spaces.
Fixed point theorems for d-complete topological spaces I
Troy L. Hicks
1992-01-01
Full Text Available Generalizations of Banach's fixed point theorem are proved for a large class of non-metric spaces. These include d-complete symmetric (semi-metric spaces and complete quasi-metric spaces. The distance function used need not be symmetric and need not satisfy the triangular inequality.
FIXED POINTS THEOREMS IN MULTI-METRIC SPACES
Laurentiu I. Calmutchi
2011-07-01
Full Text Available The aim of the present article is to give some general methods inthe fixed point theory for mappings of general topological spaces. Using the notions of the multi-metric space and of the E-metric space, we proved the analogous of several classical theorems: Banach fixed point principle, Theorems of Edelstein, Meyers, Janos etc.
Proprioceptive reflexes and neurological disorders
Schouten, A.C.
2004-01-01
Proprioceptive reflexes play an important role during the control of movement and posture. Disturbed modulation of proprioceptive reflexes is often suggested as the cause for the motoric features present in neurological disorders. In this thesis methods are developed and evaluated to quantify propri
Studies of the horizontal vestibulo-ocular reflex in spaceflight
Thornton, William E.; Uri, John J.; Moore, Tom; Pool, Sam
1989-01-01
Changes in the vestibulo-ocular reflex (VOR) during space flight have been suspected of contributing to space motion sickness. The horizontal VOR was studied in nine subjects on two space shuttle missions. Active unpaced head oscillation at 0.3 Hz was used as the stimulus to examine the gain and phase of the VOR with and without visual input, as well as the visual suppression of the reflex. No statistically significant changes were noted inflight in the gains or phase shifts of the VOR during any test condition, or between space motion sickness susceptible and nonsusceptible populations. Although VOR suppression was unaffected by spaceflight, the space motion sickness-susceptible group tended to exhibit greater error in the suppression than the nonsusceptible group. It is concluded that at this stimulus frequency, VOR gain is unaffected by space-flight, and any minor individual changes do not seem to contribute to space motion sickness.
[Reflex seizures, cinema and television].
Olivares-Romero, Jesús
2015-12-16
In movies and television series are few references to seizures or reflex epilepsy even though in real life are an important subgroup of total epileptic syndromes. It has performed a search on the topic, identified 25 films in which they appear reflex seizures. Most seizures observed are tonic-clonic and visual stimuli are the most numerous, corresponding all with flashing lights. The emotions are the main stimuli in higher level processes. In most cases it is not possible to know if a character suffers a reflex epilepsy or suffer reflex seizures in the context of another epileptic syndrome. The main conclusion is that, in the movies, the reflex seizures are merely a visual reinforcing and anecdotal element without significant influence on the plot.
Acoustic reflex and general anaesthesia.
Farkas, Z
1983-01-01
Infant and small children are not always able to cooperate in impedance measurements. For this reason it was decided, -in special cases, -to perform acoustic reflex examination under general anaesthesia. The first report on stapedius reflex and general anaesthesia was published by Mink et al. in 1981. Under the effect of Tiobutabarbital, Propanidid and Diazepam there is no reflex response. Acoustic reflex can be elicited with Ketamin-hydrochlorid and Alphaxalone-alphadolone acetate narcosis. The reflex threshold remains unchanged and the amplitude of muscle contraction is somewhat increased. The method was used: 1. to assess the type and degree of hearing loss in children with cleft palate and/or lip prior to surgery. 2. to exclude neuromuscular disorders with indication of pharyngoplasties. 3. to quantify hearing level in children--mostly multiply handicapped--with retarded speech development. The results of Behavioral Observation and Impedance Audiometry are discussed and evaluated.
Nearly Quadratic n-Derivations on Non-Archimedean Banach Algebras
Madjid Eshaghi Gordji
2012-01-01
Full Text Available Let n>1 be an integer, let A be an algebra, and X be an A-module. A quadratic function D:A→X is called a quadratic n-derivation if D(∏i=1nai=D(a1a22⋯an2+a12D(a2a32⋯an2+⋯+a12a22⋯an−12D(an for all a1,...,an∈A. We investigate the Hyers-Ulam stability of quadratic n-derivations from non-Archimedean Banach algebras into non-Archimedean Banach modules by using the Banach fixed point theorem.
Survey on nonlocal games and operator space theory
Palazuelos, Carlos, E-mail: cpalazue@mat.ucm.es [Instituto de Ciencias Matemáticas (ICMAT), Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Madrid (Spain); Vidick, Thomas, E-mail: vidick@cms.caltech.edu [Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, California 91125 (United States)
2016-01-15
This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states.
Edel Roddy
2016-05-01
Full Text Available Context: Some uncertainty surrounds both the definition and the application of reflexivity in participatory research and practice development. There is scope for further exploration of what reflexivity might look like in practice, and how the researcher/practice developer and participants might be involved. This paper does this in the context of a study that is using appreciative inquiry to explore the experience of inspection in care homes. Aims: I will explore my personal journey into the use of a relational constructionist approach to reflexivity and suggest that the 7 Cs of caring conversations provide a useful framework to inform reflexive practice. The 7 Cs will be used as a framework for the telling of this story. Implications for practice: Relational reflexivity has the potential to create the space for all those involved in research/practice development initiatives to voice their thoughts and feelings about the initiative and their involvement in it The 7 Cs of caring conversations can provide a framework for developing questions that may serve as a starting point for cultivating reflexive practice
More on (,-Normal Operators in Hilbert Spaces
Rasoul Eskandari
2012-01-01
Full Text Available We study some properties of (,-normal operators and we present various inequalities between the operator norm and the numerical radius of (,-normal operators on Banach algebra ℬ(ℋ of all bounded linear operators ∶ℋ→ℋ, where ℋ is Hilbert space.
Oculocardiac reflex during strabismus surgery
Mehryar Taghavi Gilani
2016-12-01
Full Text Available The activation of oculucardiac reflex (OCR is common during the strabismus surgeries. OCR is known as a trigemino-vagal reflex, which leads to the various side effects including bradycardia, tachycardia, arrhythmia, or in some cases cardiac arrest. This reflex could be activated during intraorbital injections, hematomas, and mechanical stimulation of eyeball and extraocular muscles surgeries. The incidence of OCR varies in a wide range, from 14% to 90%, that depends on anesthetic strategy and drug used for the surgery. The efficacy of various anticholinergic and anesthetic agents on declining the OCR reflex has been evaluated in different studies, especially in children. Although the detection of OCR goes back to 1908, its exact effect is not well recognized during strabismus surgery. In this review, we aimed to summarize the studies investigated the efficacy and potential of various anesthetic medications on inhibiting the OCR in children undergoing strabismus surgery.
Soleus stretch reflex during cycling
Grey, Michael James; Pierce, C. W.; Milner, T. E.
2001-01-01
The modulation and strength of the human soleus short latency stretch reflex was investigated by mechanically perturbing the ankle during an unconstrained pedaling task. Eight subjects pedaled at 60 rpm against a preload of 10 Nm. A torque pulse was applied to the crank at various positions during...... the crank cycle, producing ankle dorsiflexion perturbations of similar trajectory. The stretch reflex was greatest during the power phase of the crank cycle and was decreased to the level of background EMG during recovery. Matched perturbations were induced under static conditions at the same crank angle...... and background soleus EMG as recorded during the power phase of active pedaling. The magnitude of the stretch reflex was not statistically different from that during the static condition throughout the power phase of the movement. The results of this study indicate that the stretch reflex is not depressed during...
SYSTEM REFLEXIVE STRATEGIC MARKETING MANAGEMENT
A. Dligach
2013-10-01
Full Text Available This article reviews the System Reflexive paradigm of strategic marketing management, being based on the alignment of strategic economic interests of stakeholders, specifically, enterprise owners and hired managers, and consumers. The essence of marketing concept of management comes under review, along with the strategic management approaches to business, buildup and alignment of economic interests of business stakeholders. A roadmap for resolving the problems of modern marketing is proposed through the adoption of System Reflexive marketing theory.
Ternary Weighted Function and Beurling Ternary Banach Algebra l1ω(S
Mehdi Dehghanian
2011-01-01
Full Text Available Let S be a ternary semigroup. In this paper, we introduce our notation and prove some elementary properties of a ternary weight function ω on S. Also, we make ternary weighted algebra l1ω(S and show that l1ω(S is a ternary Banach algebra.
Universal Jensen's Equations in Banach Modules over a C*-Algebra and Its Unitary Group
Chun Gil PARK
2004-01-01
In this paper, we prove the generalized Hyers-Ulam-Rassias stability of universal Jensen's equations in Banach modules over a unital C*-algebra. It is applied to show the stability of universal Jensen's equations in a Hilbert module over a unital C*-algebra. Moreover, we prove the stability of linear operators in a Hilbert module over a unital C*-algebra.
Solvability of the $H^\\infty$ algebraic Riccati equation in Banach algebras
Sasane, Amol
2011-01-01
Let $R$ be a commutative complex unital semisimple Banach algebra with the involution $\\cdot ^\\star$. Sufficient conditions are given for the existence of a stabilizing solution to the $H^\\infty$ Riccati equation when the matricial data has entries from $R$. Applications to spatially distributed systems are discussed.
Stability of a Bi-Additive Functional Equation in Banach Modules Over a C⋆-Algebra
Won-Gil Park
2012-01-01
Full Text Available We solve the bi-additive functional equation f(x+y,z−w+f(x−y,z+w=2f(x,z−2f(y,w and prove that every bi-additive Borel function is bilinear. And we investigate the stability of a bi-additive functional equation in Banach modules over a unital C⋆-algebra.
Cox, S.G.
2012-01-01
The thesis deals with various aspects of the study of stochastic partial differential equations driven by Gaussian noise. The approach taken is functional analytic rather than probabilistic: the stochastic partial differential equation is interpreted as an ordinary stochastic differential equation i
Star product realizations of kappa-Minkowski space
Durhuus, Bergfinnur; Sitarz, Andrzej
2013-01-01
We define a family of star products and involutions associated with κ -Minkowski space. Applying corresponding quantization maps we show that these star products restricted to a certain space of Schwartz functions have isomorphic Banach algebra completions. For two particular star products it is ...
On the injective tensor product of M-embedded spaces
T. S. S. R. K. Rao
1993-05-01
Full Text Available We exhibit classes of Banach spaces X which are M-embedded i.e., when X is canonically embedded in X**. X is an M-ideal in X**, for which the injective tensor product is again an M-embedded space.
ON TOPOLOGICAL LINEAR CONTRACTIONS ON NORMED SPACES AND APPLICATION
SHIHMAU-HSIAN; TAMPING-KWAN; TANKOK-KEONG
1999-01-01
Shlnultaneous contractificttions, simultaneous proper contractification8 and scxnlgroup(countable family or finite family) of commuting operators and of non-commuting operatorsare first given. Characterizations are given for single bounded llner operator being a topo-logical proper contraction. By using complexification of a real Banach space and by applying afixed point theorem of Edelstein, it is shown that every compact topological strict contractionon a Banach space is a topological proper contraction. Finally, results on simultaneous propercontractification are applied to study the stability of a common fixed point of maps which areFr6chet differentiable at that point.
Savel'ev, S A; Saul'skaya, N B
2007-03-01
Studies on Sprague-Dawley rats using in vivo microdialysis and HPLC showed that the acquisition and performance of a classical conditioned reflex with pain reinforcement was accompanied by increases in the concentrations of citrulline (a side product of nitric oxide formation) and arginine (the substrate of NO synthase) in the intercellular space of the nucleus accumbens. During extinction of the reflex, there was a decrease in the elevation of extracellular citrulline in this brain structure, which correlated with the extent of extinction of the reflex. Recovery of the reflex led to increases in arginine and citrulline levels in the nucleus accumbens. These data suggest that there is an increase in nitric oxide production in the nucleus accumbens during the acquisition and performance of a classical conditioned reflex with pain reinforcement, which decreases as the reflex is extinguished and recovers with recovery of the reflex.
A note on mutiplication operators on Köthe-Bochner spaces
S. S. Khurana
2012-01-01
Let (Ω, A, μ) is a finite measure space, E an order continuous Banach function space over μ, X a Banach space and E(X) the Köthe-Bochner space. A new simple proof is given of the result that a continuous linear operator T: E(X) ® E(X) is a multiplication operator (by a function in L¥) iff T(g x) =g x for everyg Î L¥, f Î E(X), x Î X, x* Î X*.
Weak Precompactness in the Space of Vector-Valued Measures of Bounded Variation
Ioana Ghenciu
2015-01-01
Full Text Available For a Banach space X and a measure space (Ω,Σ, let M(Ω,X be the space of all X-valued countably additive measures on (Ω,Σ of bounded variation, with the total variation norm. In this paper we give a characterization of weakly precompact subsets of M(Ω,X.
The isometric extension of “into” mappings on unit spheres of AL-spaces
2008-01-01
In this paper, we show that if V0 is an isometric mapping from the unit sphere of an AL-space onto the unit sphere of a Banach space E, then V0 can be extended to a linear isometry defined on the whole space.
Outside home. Notes on reflexivity
Mara Clemente
2017-01-01
The paper proffers the idea in which a “reflexive process” on subjectivity can involve and/or hopefully involve the entire experience of the researcher, going beyond the borders of a single research. In the process, unexpected elements of subjectivity can come into play; in other cases the meaning attributed to them can change in time or can have a role different from what had been expected. Some elements, objects of epistemological analyses, as imposed by a reflexive approach, can become objects of attention also on the phenomenological level.
The history of examination of reflexes.
Boes, Christopher J
2014-12-01
In the late 1800s, Wilhelm Erb, Joseph Babinski, William Gowers, and others helped develop the neurologic examination as we know it today. Erb was one of the first to emphasize a detailed and systematic neurologic exam and was co-discoverer of the muscle stretch reflex, Gowers began studying the knee jerk shortly after it was described, and Babinski focused on finding reliable signs that could differentiate organic from hysterical paralysis. These physicians and others emphasized the bedside examination of reflexes, which have been an important part of the neurologic examination ever since. This review will focus on the history of the examination of the following muscle stretch and superficial/cutaneous reflexes: knee jerk, jaw jerk, deep abdominal reflexes, superficial abdominal reflexes, plantar reflex/Babinski sign, and palmomental reflex. The history of reflex grading will also be discussed.
Educating the Reflexive Practitioner
Marc J. Neveu
2012-09-01
wearing any clothes.Notwithstanding such issues, I do believe the studio holds the potentialto be an empowering learning experience. The intention of this article is to question the mode of instruction in an architectural studio. I’ve structured the paper in three parts. First, I will briefly describe the findingsof the study made by the Carnegie Foundation for the Advancementof Teaching known as the Boyer Report.2 To develop and support the findings of the Boyer Report, I introduce the work of the educator Donald Schön. Though I see much merit in the Boyer Report, and Schön’sproposals, I argue that a more nuanced approach is required. I will recommend, therefore, in the second section of this paper that a meansof architectural education as based on the Socratic method may be amore productive approach. My reading of the Socratic method is basedprimarily on early Socratic dialogues and I will specifically use Charmidesto illustrate the issues that I believe are relevant to studio pedagogy.3 From my analysis of Charmides I will, in the third section of the essay,describe how the Socratic method is beneficial to studio pedagogy threeways: reflexive, non-propositional, and finally how Socrates’ approachmay indeed be practical. This last section will be illustrated with a studentproject. It is my conjecture that the Socratic method offers insight intocurrent discussions of educational theory, namely student-centered,project-based learning.
陈利国; 罗成
2009-01-01
Let X be a real linear space,P be a family of separated seminorms on X,(X,T_P) denote the locally convex space generated by P,and the dual (X,P) denote the space X that has the topolopy T_P generated by the seminorm family P.The notions of uniformly extreme convex and uniformly extreme smooth for dual (X,P) are introduced,and their dual relationship is proved.The relationship with the other convexity (smoothness) are discussed.In addition,on the conditions of P-reflexivity,the dual theorem between uniformly extreme convexity and uniformly extreme smoothness is obtained,and thus the notions and results are generalized in Banach spaces.%设X是一个实线性空间,P是X上的一可分离的半范数族,(X,T_P)表示由P生成的局部凸空间,(X,P)为一个偶对.引入偶对(X,P)为一致极凸和一致极光滑的概念,并证明它们具有对偶关系,讨论了与其它几种凸性(光滑性)之间的关系,另外,在P-自反的条件下给出它们之间的对偶定理,从而推广了Banach空间相应概念和结果.
方习年
2001-01-01
本文通过引入B-NUC Banach空间及WB性质,进一步研究Banach-Saks性质(BSP)与近一致凸及紧完全凸性之间的关系.得到以下主要结果: 1)Banach空间X具有WB性质当且仅当X具有WBanach-Saks性质(WBSP); 2)X是B-NUC空间当且仅当X是具BSP的NUC空间; 3)若X具BSP及(H)性质,则X是CωR空间(紧完全ω-凸空间).
[Clinical relevance of cardiopulmonary reflexes in anesthesiology].
Guerri-Guttenberg, R A; Siaba-Serrate, F; Cacheiro, F J
2013-10-01
The baroreflex, chemoreflex, pulmonary reflexes, Bezold-Jarisch and Bainbridge reflexes and their interaction with local mechanisms, are a demonstration of the richness of cardiovascular responses that occur in human beings. As well as these, the anesthesiologist must contend with other variables that interact by attenuating or accentuating cardiopulmonary reflexes such as, anesthetic drugs, surgical manipulation, and patient positioning. In the present article we review these reflexes and their clinical relevance in anesthesiology.
孟京华
2004-01-01
给出了A型和B型均一致凸Banach空间概论,证明了:一致凸Banach空间是A型平均一致凸的,A型平均一致凸Banach空间X是弱局部一致凸和严格凸的;B型平均一致凸Banach空间X任意元在以0为顶点的闭凸锥中有惟一最佳逼近.
Reflexive fatherhood in everyday life
Westerling, Allan
2015-01-01
This article looks at fathering practices in Denmark, using the findings from a research project on everyday family life in Denmark. It takes a social psychological perspective and employs discursive psychology and theories about reflexive modernisation. It shows how fathers orient towards intimacy...
The reflexive case study method
Rittenhofer, Iris
2015-01-01
This paper extends the international business research on small to medium-sized enterprises (SME) at the nexus of globalization. Based on a conceptual synthesis across disciplines and theoretical perspectives, it offers management research a reflexive method for case study research of postnational...
Modified van der Pauw method based on formulas solvable by the Banach fixed point method
2012-01-01
We propose a modification of the standard van der Pauw method for determining the resistivity and Hall coefficient of flat thin samples of arbitrary shape. Considering a different choice of resistance measurements we derive a new formula which can be numerically solved (with respect to sheet resistance) by the Banach fixed point method for any values of experimental data. The convergence is especially fast in the case of almost symmetric van der Pauw configurations (e.g., clover shaped samples).
An Ordinal Index on the Space of Strictly Singular Operators
Beanland, Kevin
2009-01-01
Using the notion of $S_\\xi$-strictly singular operator introduced by Androulakis, Dodos, Sirotkin and Troitsky, we define an ordinal index on the subspace of strictly singular operators between two separable Banach spaces. In our main result, we provide a sufficient condition implying that this index is bounded by $\\omega_1$. In particular, we apply this result to study operators on totally incomparable spaces, hereditarily indecomposable spaces and spaces with few operators.
Continuity of Extremal Elements in Uniformly Convex Spaces
Ferguson, Timothy
2013-01-01
In this paper, we study the problem of finding the extremal element for a linear functional over a uniformly convex Banach space. We show that a unique extremal element exists and depends continuously on the linear functional, and vice versa. Using this, we simplify and clarify Ryabykh's proof that for any linear functional on a uniformly convex Bergman space with kernel in a certain Hardy space, the extremal functional belongs to the corresponding Hardy space.
Certain Sequence Spaces over the Non-Newtonian Complex Field
Sebiha Tekin; Feyzi Başar
2013-01-01
It is known from functional analysis that in classical calculus, the sets $\\omega $ , ${\\ell }_{\\mathrm{\\infty }}$ , $c$ , ${c}_{\\mathrm{0}}$ and ${\\ell }_{p}$ of all bounded, convergent, null and $p$ -absolutely summable sequences are Banach spaces with their natural norms and they are complete according to the metric reduced from their norm, where $0
THE FUNCTIONAL DIMENSION OF SOME CLASSES OF SPACES
LIU SHANGPING; LI BINGREN
2005-01-01
The functional dimension of countable Hilbert spaces has been discussed by some authors. They showed that every countable Hilbert space with finite functional dimension is nuclear. In this paper the authors do further research on the functional dimension, and obtain the following results: (1) They construct a countable Hilbert space, which is nuclear, but its functional dimension is infinite. (2) The functional dimension of a Banach space is finite if and only if this space is finite dimensional. (3)Let B be a Banach space, B* be its dual, and denote the weak * topology of B* by σ(B*, B). Then the functional dimension of (B*, σ(B*, B)) is 1. By the third result, a class of topological linear spaces with finite functional dimension is presented.
Random fixed points of non-self maps and random approximations
Ismat Beg
1997-01-01
Full Text Available In this paper we prove random fixed point theorems in reflexive Banach spaces for nonexpansive random operators satisfying inward or Leray-Schauder condition and establish a random approximation theorem.
Generalized Köthe-Toeplitz Duals of Some Vector-Valued Sequence Spaces
Yılmaz Yılmaz
2013-01-01
Full Text Available We know from the classical sequence spaces theory that there is a useful relationship between continuous and -duals of a scalar-valued FK-space originated by the AK-property. Our main interest in this work is to expose relationships between the operator space and and the generalized -duals of some -valued AK-space where and are Banach spaces and . Further, by these results, we obtain the generalized -duals of some vector-valued Orlicz sequence spaces.
陈利国; 罗成
2011-01-01
首先引入局部凸空间的k-一致极凸性和k-一致极光滑性这一对对偶概念,它们既是Banach空间κ-一致极凸性和k-一致极光滑性推广,又是局部凸空间一致极凸性和一致极光滑性的自然推广.其次讨论它们与其它k-凸性(k-光滑性)之间的关系.最后,在p-自反的条件下给出它们之间的等价对偶定理.%The dual notions of fc-uniformly extreme convexity and fc-uniformly extreme smoothness are introduced In locally convex spaces, which are generalization of both k-uniformly extreme convexity (fc-uniformly extreme smoothness) in Banach spaces and uniformly extreme convexity (uniformly extreme smoothness) In locally convex spaces. The relationship between them and the other convexity (smoothness) are discussed. In addition, on the conditions of P-reflexivity, we obtain further the equivalent dual theorem of between fc-uniformly extreme convexity and k- uniformly extreme smoothness.
Integrating Reflexivity in Livelihoods Research
Prowse, Martin
2010-01-01
Much poverty and development research is not explicit about its methodology or philosophical foundations. Based on the extended case method of Burawoy and the epistemological standpoint of critical realism, this paper discusses a methodological approach for reflexive inductive livelihoods researc...... that overcomes the unproductive social science dualism of positivism and social constructivism. The approach is linked to a conceptual framework and a menu of research methods that can be sequenced and iterated in light of research questions.......Much poverty and development research is not explicit about its methodology or philosophical foundations. Based on the extended case method of Burawoy and the epistemological standpoint of critical realism, this paper discusses a methodological approach for reflexive inductive livelihoods research...
Reflexivity in Narratives on Practice
Jakobsen, Helle Nordentoft; Olesen, Lektor Birgitte Ravn
Previous research has shown how reflexivity is a precondition for knowledge co-production through productive dialogue in organisational contexts because it entails a re-ordering, re-arranging and re-designing of what one knows and therefore creates new angles of vision. In this paper, we draw...... on Bakhtinian dialogic communication theory and discursive psychology to investigate the written practice narratives of 23 students on a Masters Degree Programme in Educational Studies, focusing on how the process of writing narratives accentuates reflexivity. Our findings indicate that the narratives invite...... a dialogic conception of practice as they entail a conceptual reframing of key elements in practice. In addition, the narratives expose a situational and relational, rather than normative, focus which allows for reflections on emotional and bodily experiences. In conclusion, we argue that practice narratives...
Integrating Reflexivity in Livelihoods Research
Prowse, Martin
2010-01-01
Much poverty and development research is not explicit about its methodology or philosophical foundations. Based on the extended case method of Burawoy and the epistemological standpoint of critical realism, this paper discusses a methodological approach for reflexive inductive livelihoods researc...... that overcomes the unproductive social science dualism of positivism and social constructivism. The approach is linked to a conceptual framework and a menu of research methods that can be sequenced and iterated in light of research questions....
ON PROBLEM OF NEAREST COMMON FIXED POINT OF NONEXPANSIVE MAPPINGS
ZHANG Shi-sheng
2006-01-01
The purpose is by using the viscosity approximation method to study the convergence problem of the iterative scheme for an infinite family of nonexpansive mappings and a given contractive mapping in a reflexive Banach space. Under suitable conditions,it was proved that the iterative sequence converges strongly to a common fixed point which was also the unique solution of some variational inequality in a reflexive Banach space. The results presented extend and improve some recent results.
Sunder, V S
2016-01-01
The primarily objective of the book is to serve as a primer on the theory of bounded linear operators on separable Hilbert space. The book presents the spectral theorem as a statement on the existence of a unique continuous and measurable functional calculus. It discusses a proof without digressing into a course on the Gelfand theory of commutative Banach algebras. The book also introduces the reader to the basic facts concerning the various von Neumann–Schatten ideals, the compact operators, the trace-class operators and all bounded operators. .
Lipschitz spaces and bounded mean oscillation of harmonic mappings
Chen, Sh; Vuorinen, M; Wang, X
2012-01-01
In this paper, we first study the bounded mean oscillation of planar harmonic mappings, then a relationship between Lipschitz-type spaces and equivalent modulus of real harmonic mappings is established. At last, we obtain sharp estimates on Lipschitz number of planar harmonic mappings in terms of bounded mean oscillation norm, which shows that the harmonic Bloch space is isomorphic to $BMO_{2}$ as a Banach space.