Opial modulus, moduli of noncompact convexity and fixed points for asymptotically regular mappings
type: Item
instance of: scholarly article
title: Opial modulus, moduli of noncompact convexity and fixed points for asymptotically regular mappings
zbMATH Open document ID: 0961.47036
DOI: 10.1016/S0362-546X(98)00300-9
author: R. Smith
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-05-21T00:00:00Z
review text: Let \(C\) be a nonempty closed bounded convex subset of a Banach space. A map \(T: C \rightarrow C\) is said to be asymptotically regular if \(\lim_n\|T^{n+1}x - T^nx\|= 0\) for every \(x \in C\). Sufficient conditions for the existence of fixed points of asymptotically regular maps are given in the terms of the weakly convergent sequence coefficient, the Opial's modulus and moduli of noncompact convexity.
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 1512498
zbMATH Keywords: fixed point
zbMATH Keywords: asymptotically regular mapping
zbMATH Keywords: measure of noncompactness
zbMATH Keywords: Opial property
zbMATH Keywords: nonexpansive mapping
zbMATH Keywords: modulus of noncompact convexity
reviewed by: Valerii V. Obukhovskij
MaRDI profile type: Publication
full work available at URL: s0362-546x(98)00300-9
OpenAlex ID: W2051353800
description: scientific article; zbMATH DE number 1512498