Weak uniform normal structure and fixed points of asymptotically regular semigroups
type: Item
instance of: scholarly article
title: Weak uniform normal structure and fixed points of asymptotically regular semigroups
zbMATH Open document ID: 1095.47007
author: Luchuan Zeng
publication date: 2006-01-05T00:00:00Z
review text: Let \(X\) be a Banach space with a weak uniform normal structure and let \(C\) be some (nonempty) convex weakly compact subset of it. Then each asymptotically regular semigroup \(T=(T(t);t\in S)\) of weakly continuous selfmaps on \(C\) with \(\liminf_{S\ni t\to \infty} L(T(t))< WCS(X)\) has a common fixed point. Here, \(L(T(t))\) is the exact Lipschitz constant of \(T(t)\) and \(WCS(X)\) is the weakly convergent sequence coefficient of \(X\).
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47H20
zbMATH DE Number: 2243672
zbMATH Keywords: Banach space
zbMATH Keywords: weak uniform normal structure
zbMATH Keywords: exact Lipschitz constant
zbMATH Keywords: weakly convergent sequence coefficient
zbMATH Keywords: asymptotically regular semigroup
zbMATH Keywords: convex weakly compact subset
zbMATH Keywords: common fixed point
reviewed by: Mihai Turinici
MaRDI profile type: Publication
full work available at URL: s10114-004-0402-7
OpenAlex ID: W2045481334
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DOI: 10.1007/S10114-004-0402-7
published in: Acta Mathematica Sinica, English Series
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description: scientific article