Cyclic algorithm for common fixed points of finite family of strictly pseudocontractive mappings of Browder-Petryshyn type
type: Item
instance of: scholarly article
title: Cyclic algorithm for common fixed points of finite family of strictly pseudocontractive mappings of Browder-Petryshyn type
zbMATH Open document ID: 1180.47044
author: J. Martínez
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-04-14T00:00:00Z
review text: The authors prove weak and strong convergence theorems for finitely many strict pseudocontractions \(T_1,\dots,T_N\) of a closed convex subset \(K\) of a 2-uniformly smooth and uniformly convex Banach space by the iterative scheme: \(x_1\in K\) and \(x_{n+1}=\alpha_n x_n+(1-\alpha_n)T_{n\text{mod}\,N}\), where \(\{\alpha_n\}\) is an appropriate sequence in \([0,1]\). A necessary and sufficient condition for the strong convergence of the sequence \(\{x_n\}\) to a common fixed point of the family of mappings is also proved.
reviewed by: Satit Saejung
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 65J15
zbMATH DE Number: 5543761
zbMATH Keywords: fixed points
zbMATH Keywords: strictly pseudocontractive maps
zbMATH Keywords: cyclic algorithm
zbMATH Keywords: \(q\)-uniformly smooth Banach spaces
MaRDI profile type: Publication
full work available at URL: j.na.2008.07.015
OpenAlex ID: W2055651394
cites work: Iterative methods for strict pseudo-contractions in Hilbert spaces
cites work: Construction of fixed points of nonlinear mappings in Hilbert space
cites work: A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces
cites work: Demiclosedness principle and convergence theorems for strictly pseudocontractive mappings of Browder-Petryshyn type
cites work: Q4547144
cites work: Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces
cites work: Inequalities in Banach spaces with applications
DOI: 10.1016/J.NA.2008.07.015
description: scientific article; zbMATH DE number 5543761