On the fixed points of affine nonexpansive mappings
type: Item
instance of: scholarly article
title: On the fixed points of affine nonexpansive mappings
zbMATH Open document ID: 1021.47035
DOI: 10.1155/S016117120100638X
author: Hülya Duru
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2002-08-13T00:00:00Z
full work available at URL: https://eudml.org/doc/50331
full work available at URL: S016117120100638X.html
review text: Let \(K\) be a closed bounded subset of a Banach space \(X\) and let \(T:K\to K\) be a continuous affine mapping. It is proved that: (1) if \(T\) is nonexpansive, then it has a fixed point; (2) if \(T\) has only one fixed point, then the mapping \(A=(I+T)/2\) is a focusing mapping; (3) a continuous mapping \(S:K\to K\) has a fixed point if and only if, for each \(x\in K\), \(\|(A^n\circ S)(x)-(S\circ A^n)(x)\|\to 0\) for some strictly nonexpansive affine mapping \(T\).
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 1780307
zbMATH Keywords: affine nonexpansive mapping
zbMATH Keywords: existence of fixed points
zbMATH Keywords: Banach space
zbMATH Keywords: continuous affine mapping
zbMATH Keywords: focusing mapping
reviewed by: Alexandra Rodkina
MaRDI profile type: Publication
OpenAlex ID: W2149761118
description: scientific article; zbMATH DE number 1780307