Results 211 to 220 of about 9,111 (245)

A Remark on Nonexpansive Mappings

Canadian Mathematical Bulletin, 1981
Let X be a closed convex subset of a Banach space and let T: X → X be a nonexpansive mapping, i.e.
Malgorzata Koter, Kazimierz Goebel
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Nonexpansive and locally nonexpansive mappings in product spaces

Nonlinear Analysis: Theory, Methods & Applications, 1988
Let E and F be Banach spaces with \(X\subset E\) and \(Y\subset F\).
William A. Kirk, C. M. Yanez
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Fixed points of nonexpansive and quasi-nonexpansive mappings

The Journal of Analysis, 2018
In the paper Krasnoselskii–Mann method for non-self mappings in the journal of Fixed Point Theory and Applications, Colao and Marino proved strong convergence of Krasnoselskii–Mann algorithm defined by $$x_{n+1}=\alpha _nx_n+(1-\alpha _n)Tx_n$$
M. Sankara Narayanan, M. Marudai
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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.
Tae-Hwa Kim, Hong-Kun Xu
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On Asymptotically Nonexpansive Semigroups of Mappings

Canadian Mathematical Bulletin, 1970
A selfmapping f of a metric space (X, d) is nonexpansive (ε-nonexpansive) if d(f(x), f(y)) ≤ d(x, y) for all x, y ∊ X (respectively if d(x, y) < ε). In [1], M.
R. D. Holmes, P. P. Narayanaswami
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On the asymptotic regularity of nonexpansive mappings [PDF]

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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Fixed points of nonexpansive mappings

Journal of Mathematical Sciences, 1996
This is a brief, but very informative survey article of the basic results concerning the question of existence of fixed points of nonexpansive mappings in Banach spaces. The structure of this article is the following: Introduction. Principal notations. Chapter 1: Normal structure in Banach spaces and its generalizations; 1.1.
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An inequality concerning nonexpansive mappings [PDF]

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 1996
In recent results concerning nonexpansive maps and the problem of iteratively solving nonlinear equations of the form Qx=y in a Hilbert space (application areas include networks and signal processing), a certain inequality plays a central role. Here we consider the case in which Q is continuously Frechet differentiable and we give criteria under which ...
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Rigidity properties of nonexpansive mappings

Nonlinear Analysis: Theory, Methods & Applications, 1987
This paper is concerned with existence questions for nonexpansive retraction maps onto linear subspaces of Banach spaces and some related topics (like metric projections, contractive linear projections, and Korovkin shadows). Mainly for the spaces C[0,1] and \(L_ 1[0,1]\), the author proves nonexistence results for nonexpansive retractions, as well as ...
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The cluster set of a nonexpansive mapping

Rendiconti del Seminario Matematico e Fisico di Milano, 1987
Summary: For a nonexpansive mapping q: \({\mathbb{R}}^ d\to {\mathbb{R}}^ d\), we examine some properties of the set S of all possible limit points of sequences of the form x, \(q(x),q^ 2(x),... \). We then characterize those piecewise isometric nonexpansive mappings having the property: for every x there exists a finite k such that \(q^ k(x)\in S\).
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