Convergence theorems for three finite families of multivalued nonexpansive mappings
type: Item
instance of: scholarly article
title: Convergence theorems for three finite families of multivalued nonexpansive mappings
zbMATH Open document ID: 1318.47068
author: Rashwan Ahmed
author: Saeed Altwqi
published in: Journal of the Egyptian Mathematical Society
publication date: 2014-11-03T00:00:00Z
review text: Let \(K\) be a nonempty closed convex subset of a uniformly convex Banach space \(E\) and \(T_i, S_i, R_i:K\rightarrow CB(K)\), \(i=1,2,\dots,k\), be three finite families of multivalued nonexpansive mappings from \(K\) into \(CB(K)\), the collection of all nonempty closed bounded subsets of \(E\), such that \[ F:=(\bigcap_{i=1}^{k} \mathrm{Fix}\,(T_i))\cap (\bigcap_{i=1}^{k} \mathrm{Fix}\,(S_i))\cap (\bigcap_{i=1}^{k} \mathrm{Fix}\,(R_i)) \neq \emptyset, \] where \( \mathrm{Fix}\,(T_i)\) denotes the set of fixed points of \(T_i\). In order to approximate a common fixed point \(p\in F\), the authors consider a three step iterative scheme for which they prove weak and strong convergence theorems.
reviewed by: Vasile Berinde
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 6363318
zbMATH Keywords: uniformly convex Banach space
zbMATH Keywords: multivalued nonexpansive mapping
zbMATH Keywords: fixed point
zbMATH Keywords: three step iterative scheme
zbMATH Keywords: convergence theorem
zbMATH Keywords: weak convergence
MaRDI profile type: Publication
full work available at URL: j.joems.2013.10.008
OpenAlex ID: W2092950249
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DOI: 10.1016/J.JOEMS.2013.10.008
description: scientific article; zbMATH DE number 6363318