Iterative Schemes for Fixed Points of Relatively Nonexpansive Mappings and Their Applications [PDF]
, 2010 We present two iterative schemes with errors which are proved to be strongly convergent to a common element of the set of fixed points of a countable family of relatively nonexpansive mappings and the set of fixed points of nonexpansive mappings in the ...
Somyot Plubtieng, Wanna Sriprad
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Fixed Point for Uniformly Local Asymptotic Nonexpansive Map [PDF]
arXiv, 2023 Fixed points for uniformly local asymptotic nonexpansive maps are discussed in this article. An approximate fixed point sequence for such a map over a uniformly convex Banach space is derived. At the end, we study the unique fixed point for uniformly local asymptotic contraction.
arxiv
Approximating common solutions of variational inequalities by iterative algorithms with applications [PDF]
, 2011 In this paper, we introduce an iterative scheme for a general variational inequality. Strong convergence theorems of common solutions of two variational inequalities are established in a uniformly convex and 2-uniformly smooth Banach space.
Sun Young Cho, Xiaolong Qin, Yeol Je Cho
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The Daugavet equation in uniformly convex Banach spaces
Journal of Functional Analysis, 1991 AbstractIt is shown that a continuous operator T: X → X on a uniformly convex Banach space satisfies the Daugavet equation ∥I + T∥ = 1 + ∥T∥ if and only if the norm ∥T∥ of the operator lies in the spectrum of T. Specializing this result to compact operators, we see that a compact operator on a uniformly convex Banach space satisfies the Daugavet ...
Charalambos D. Aliprantis +2 more
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A universal reflexive space for the class of uniformly convex Banach spaces [PDF]
Mathematische Annalen, 2006 We show that there exists a separable reflexive Banach space into which every separable uniformly convex Banach space isomorphically embeds. This solves a problem of J. Bourgain. We also give intrinsic characterizations of separable reflexive Banach spaces which embed into a reflexive space with a block $q$-Hilbertian and/or a block $p$-Besselian ...
Th. Schlumprecht, Edward Odell
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Mann-Type Viscosity Approximation Methods for Multivalued Variational Inclusions with Finitely Many Variational Inequality Constraints in Banach Spaces [PDF]
, 2013 We introduce Mann-type viscosity approximation methods for finding solutions of a multivalued variational inclusion (MVVI) which are also common ones of finitely many variational inequality problems and common fixed points of a countable family of ...
Abdul Latif +2 more
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Corrigendum to "Approximation by C^{p}-smooth, Lipschitz functions on Banach spaces" [J. Math. Anal. Appl., 315 (2006), 599-605] [PDF]
, 2008 In this erratum, we recover the results from an earlier paper of the author's which contained a gap. Specifically, we prove that if X is a Banach space with an unconditional basis and admits a C^{p}-smooth, Lipschitz bump function, and Y is a convex ...
Azagra, Johanis, R. Fry
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Examples of k-iterated spreading models
, 2011 It is shown that for every $k\in\mathbb{N}$ and every spreading sequence $\{e_n\}_{n\in\mathbb{N}}$ that generates a uniformly convex Banach space $E$, there exists a uniformly convex Banach space $X_{k+1}$ admitting $\{e_n\}_{n\in\mathbb{N}}$ as a $k+1$-
Argyros, Spiros A., Motakis, Pavlos
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Oscillation and the mean ergodic theorem for uniformly convex Banach spaces [PDF]
Ergodic Theory and Dynamical Systems, 2014 AbstractLet $ \mathbb{B} $ be a $p$-uniformly convex Banach space, with $p\geq 2$. Let $T$ be a linear operator on $ \mathbb{B} $, and let ${A}_{n} x$ denote the ergodic average $(1/ n){\mathop{\sum }\nolimits}_{i\lt n} {T}^{n} x$. We prove the following variational inequality in the case where $T$ is power bounded from above and below: for any ...
Jeremy Avigad, Jason Rute
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Uniformly convex operators and martingale type
, 2002 The concept of uniform convexity of a Banach space was generalized to linear operators between Banach spaces and studied by Beauzamy [1976]. Under this generalization, a Banach space X is uniformly convex if and only if its identity map I_X is.
Wenzel, J
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