Convergence theorem of common fixed points for Lipschitzian pseudo-contraction semi-groups in Banach spaces
type: Item
instance of: scholarly article
title: Convergence theorem of common fixed points for Lipschitzian pseudo-contraction semi-groups in Banach spaces
zbMATH Open document ID: 1181.47074
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 2009-05-04T00:00:00Z
review text: The author considers a uniformly convex Banach space \(E\) satisfying the Opial condition, a closed, convex subset \(C\) of \(E\), and a Lipschitzian pseudo-contractive semigroup \(\text{T}:=\{T(t):t\geq 0\}:C\to C\) such that \(\text{F}:= \bigcap_{t\geq 0}F(T(t))\neq \emptyset\), where \(F(T(t))\) denotes the set of fixed points of \(T(t)\). Let \((\alpha _n)_n\) be a sequence in \((0,1)\) and \((t_n)_n\) a sequence in \((0,\infty)\) satisfying (i) \(\limsup_{n}\alpha_n<1\) and (ii) \(\lim_nt_n=\lim_n\frac{\alpha_n}{t_n}=0\). Under these circumstances, he shows that the sequence \(x_0\in C\), \(x_n=\alpha_nx_{n-1}+(1-\alpha_n)T(t_n)x_n,\;n\geq 1\), is weakly convergent to a common fixed point of the semigroup.
reviewed by: Ioan I. Vrabie
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H20
zbMATH DE Number: 5550582
zbMATH Keywords: Lipschitzian pseudo-contractive semigroup
zbMATH Keywords: common fixed point
zbMATH Keywords: Opial condition
zbMATH Keywords: strongly pseudo-contraction mapping
zbMATH Keywords: implicit iteration process
author: Shihsen Chang
MaRDI profile type: Publication
full work available at URL: s10483-009-0202-y
OpenAlex ID: W160538844
cites work: Q4092518
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cites work: Convergence theorems of common fixed points for a finite family of Lipschitz pseudocontractions in Banach spaces
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DOI: 10.1007/S10483-009-0202-Y
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description: scientific article; zbMATH DE number 5550582