Results 121 to 130 of about 316 (157)

Strong convergence of an explicit iteration process for a totally asymptotically I-nonexpansive mapping in Banach spaces

Applied Mathematics Letters, 2010
In this work we prove the strong convergence of an explicit iterative process to a common fixed point of a totally asymptotically I-nonexpansive mapping T and a totally asymptotically nonexpansive mapping I, defined on a nonempty closed convex subset of ...
Farrukh Mukhamedov, Mansoor Saburov
exaly   +2 more sources

Convergence Theorems of Variational Inequality for Asymptotically Nonexpansive Nonself Mapping in CAT(0) Spaces

Mathematics, 2019
The aim of this manuscript is to get the strong convergence theorems of the Moudafi’s viscosity approximation methods for an asymptotically nonexpansive nonself mapping in C A T ( 0 ...
Kyung Soo Kim
exaly   +2 more sources

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Asymptotically nonexpansive mappings

Nonlinear Analysis: Theory, Methods & Applications, 1998
This is a very interesting paper. The method used suggests an entirely new approach in the study of fixed points and related properties of asymptotically nonexpansive mappings. Let \(E\) be a Banach space and \(D\subseteq E\). We recall, if there exists a sequence of reals \(\{k_i\}\) with \(k_i\downarrow 1\) such that \(\|T^ix- T^iy\|\leq k_i\|x-y\|\)
Kirk, W. A., Yañez, Carlos Martinez, Shin, Sang Sik   +2 more
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Remarks on asymptotically nonexpansive mappings

Nonlinear Analysis: Theory, Methods & Applications, 2000
It is known that the uniform convexity in every direction implies the existence of fixed points for a nonexpansive mapping \(T:C\to C\) if \(C\) is assumed to be weakly compact. It is still an open problem whether this is true for asymptotically nonexpansive mappings. The purpose of the paper is to present a partial answer to this question.
Kim, Tae-Hwa, Xu, Hong-Kun
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Asymptotic Behavior of a Periodic Sequence of Nonexpansive Mappings with Applications

Bulletin of the Belgian Mathematical Society - Simon Stevin, 2023
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Hashemi, Mehrnaz Sadat, Khatibzadeh, Hadi   +1 more
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Viscosity approximation methods for asymptotically nonexpansive mappings

Applied Mathematics and Computation, 2008
The iteration method \(x_{n+1}=\alpha_n f(x_n) + \beta_n x_n + \gamma_n T^nx_n\) is discussed for approximating a special fixed point of an asymptotically nonexpansive mapping \(T\) defined on a uniformly convex Banach space with uniformly Gâteaux differentiable norm.
Jian Lou, Li-juan Zhang, Zhen He
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Asymptotic Properties of Monotonic Nonexpansive Mappings

Discrete Event Dynamic Systems, 2004
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Asymptotic behavior for asymptotically nonexpansive mappings

Nonlinear Analysis: Theory, Methods & Applications, 1996
Let \(X\) be a Banach space. Suppose that \(X\) has the Opial (or locally uniform Opial) property and the norm of \(X\) is UKK (uniform Kadec-Klee). Let \(C\) be a weakly compact convex subset of \(X\), and let \(T\) be an asymptotically nonexpansive self-mapping of \(C\) in the weak sense.
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Pythagorean Property and Asymptotic Relatively Nonexpansive Mappings

Mediterranean Journal of Mathematics, 2018
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Gabeleh, M., Markin, J.
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On the asymptotic regularity of nonexpansive mappings

Acta Mathematica Hungarica, 1986
Given a normed vector space X, a self-mapping P of X is said to be asymptotically regular if for every point x of X we have \(\| P^{n+1}x-P^ nx\| \to 0\) as \(n\to \infty\). First, a new and simple proof is given to the theorem of S. Ishikawa, namely: Theorem B: Let D be a subset of a normed space X and \(T: X\to X\) be a nonexpansive mapping.
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