On the structure of fixed-point sets of asymptotically regular mappings in Hilbert spaces
type: Item
instance of: scholarly article
title: On the structure of fixed-point sets of asymptotically regular mappings in Hilbert spaces
zbMATH Open document ID: 1207.47058
DOI: 10.12775/TMNA.2009.049
author: Jarosław Górnicki
published in: Topological Methods in Nonlinear Analysis
publication date: 2010-07-09T00:00:00Z
review text: Let \(H\) be a Hilbert space, \(C\in X\) a nonempty bounded closed convex set, \(T: C\to C\) such that, for every \(x\in X\), \(\lim|T^n(x), T^{n+1}(x)|= 0\) and \(\liminf\| T^n(x)\|< \sqrt{2}\) if \(n\to\infty\). By using techniques of asymptotic center, the author gives an elementary proof of the existence of fixed points of \(T\) and proves that the set of fixed points of \(T\) is a retract of \(C\).
reviewed by: Delfina Roux
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 54C15
zbMATH DE Number: 5734962
zbMATH Keywords: Hilbert space
zbMATH Keywords: asymptotically regular map
zbMATH Keywords: fixed points
zbMATH Keywords: retraction
MaRDI profile type: Publication
full work available at URL: tmna.2009.049
OpenAlex ID: W2469694443
description: scientific article; zbMATH DE number 5734962