Ergodic theorems for non-Lipschitzian semigroups without convexity
type: Item
instance of: scholarly article
title: Ergodic theorems for non-Lipschitzian semigroups without convexity
zbMATH Open document ID: 0912.47030
DOI: 10.1142/S0252959902000201
author: Jipu Ma
author: Gang Li
published in: Chinese Annals of Mathematics. Series B
publication date: 1999-05-03T00:00:00Z
review text: Let \(G\) be a semitopological semigroup. Let \(C\) be a nonempty subset of a Hilbert space and \({\mathfrak I}= \{T_t:t\in G\}\) be a representation of \(G\) as asymptotically nonexpansive type mappings of \(C\) into itself such that the common fixed point set \(F({\mathfrak I})\) of \({\mathfrak I}\) in \(C\) is nonempty. It is proved that \(\bigcap_{s\in G}\overline{\text{co}}\{T_{ts}x: t\in G\}\cap F({\mathfrak I})\) is nonempty for each \(x\in C\) if and only if there exists a nonexpansive retraction \(P\) of \(C\) onto \(F({\mathfrak I})\) such that \(PT_s= T_sP= P\) for all \(s\in G\) and \(P(x)\) is in the closed convex hull of \(\{T_sx: s\in G\}\), \(x\in C\).
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H20
zbMATH DE Number: 1159360
zbMATH Keywords: ergodic theorems
zbMATH Keywords: semitopological semigroup
zbMATH Keywords: representation
zbMATH Keywords: asymptotically nonexpansive type mappings
zbMATH Keywords: nonexpansive retraction
reviewed by: Jürgen Appell
MaRDI profile type: Publication
full work available at URL: s0252959902000201
OpenAlex ID: W2316125959
description: scientific article; zbMATH DE number 1159360