Fixed points of isometries on weakly compact convex sets
type: Item
instance of: scholarly article
title: Fixed points of isometries on weakly compact convex sets
zbMATH Open document ID: 1032.47036
DOI: 10.1016/S0022-247X(03)00398-6
author: D. Massart
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-07-30T00:00:00Z
review text: Let \(K\) be a nonempty convex set in a Banach space and \(T:K\to K\) an isometry. If \(K\) is closed and bounded and if \(X\) is uniformly convex, then it is shown that the Chebyshev-center is a fixed point of \(T\). If \(X\) is arbitrary and \(K\) is weakly compact such that each nonempty closed convex subset has the fixed point property for isometries, then \(T\) has a fixed point in the Chebyshev-center of \(K\).
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 1956897
zbMATH Keywords: weakly compact convex set
zbMATH Keywords: isometry
zbMATH Keywords: fixed point
zbMATH Keywords: uniformly convex Banach space
reviewed by: Christian Fenske
MaRDI profile type: Publication
cites work: Q5786938
cites work: A Theorem on Fixed Points Under Isometries
cites work: Remarks on the fixed point problem for nonexpansive maps
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cites work: On Asymptotic Centers and Fixed Points of Nonexpansive Mappings
full work available at URL: s0022-247x(03)00398-6
OpenAlex ID: W2128008280
description: scientific article; zbMATH DE number 1956897