Weak convergence of almost orbits of asymptotically nonexpansive commutative semigroups
type: Item
instance of: scholarly article
title: Weak convergence of almost orbits of asymptotically nonexpansive commutative semigroups
zbMATH Open document ID: 1058.47049
DOI: 10.1016/S0022-247X(02)00175-0
author: Wiesława Kaczor
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-12-16T00:00:00Z
review text: Let \(X\) be a real uniformly convex Banach space whose dual space \(X^*\) has the Kadec-Klee property (i.e., for every sequence \(\{x_n\}\subset X^*\), the following implication is true: \((x_n\to x\wedge\| x_n\|\to\| x\|)\Rightarrow (\| x_n- x\|\to 0))\). Let further \(G\) be a commutative semigroup with identity, and \(\{T(t): t\in G\}\) be an asymptotically nonexpansive semigroup acting on a nonempty closed convex subset \(C\subset X\). The main result of the present paper gives three equivalent conditions for the weak convergence of almost orbits of \(\{T(t)\}\) .
Mathematics Subject Classification ID: 47H20
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 1846006
zbMATH Keywords: Kadec-Klee property
zbMATH Keywords: almost orbits
reviewed by: Khristo N. Boyadzhiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1846006