Browder's convergence for uniformly asymptotically regular nonexpansive semigroups in Hilbert spaces
type: Item
instance of: scholarly article
title: Browder's convergence for uniformly asymptotically regular nonexpansive semigroups in Hilbert spaces
zbMATH Open document ID: 1206.47058
DOI: 10.1155/2010/418030
author: Tomonari Suzuki
author: Genaro López
published in: Fixed Point Theory and Applications
publication date: 2010-04-13T00:00:00Z
full work available at URL: https://eudml.org/doc/231951
review text: Let \(C\) be a closed convex subset of a Hilbert space and \((T(t):t\geq 0)\) be a uniformly asymptotically regular nonexpansive semigroup on \(C\) with \(F:=\cap\{F(T(t)):t\geq 0\}\neq \emptyset\). Let \((a_n)\subset (0,1)\) and \((t_n)\subset (0,\infty)\) be sequences with \(\lim_n(a_n)=\lim_n(a_n/t_n)=0\). Then, for each \(u\in C\), the implicit sequence \[ x_n=a_nu+(1-a_n)T(t_n)x_n, \quad n\geq 0, \] converges strongly to an element of \(F\), nearest to \(u\).
reviewed by: Mihai Turinici
Mathematics Subject Classification ID: 47H20
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 5692331
zbMATH Keywords: Hilbert space
zbMATH Keywords: closed convex set
zbMATH Keywords: one-parameter strongly continuous semigroup of nonexpansive mappings
zbMATH Keywords: common fixed point
zbMATH Keywords: implicit sequence
zbMATH Keywords: Opial property
zbMATH Keywords: strong convergence
Wikidata QID: Q59219961
MaRDI profile type: Publication
OpenAlex ID: W2089995426
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description: scientific article; zbMATH DE number 5692331