Approximating fixed points of nonexpansive mappings

We consider a mapping S of the form S=α0I+α1T1+α2T2+⋯+αkTk, where αi≥0, α0>0, α1>0 and ∑i=0kαi=1. We show that the Picard iterates of S converge to a common fixed point of Ti(i=1,2,…,k)in a Banach space when Ti(i=1,2,…,k) are nonexpansive.

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Bibliographic Details
Main Authors: Guimei Liu, Deng Lei, Shenghong Li
Format: Article
Language:English
Published: Wiley 2000-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171200003252
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author Guimei Liu
Deng Lei
Shenghong Li
author_facet Guimei Liu
Deng Lei
Shenghong Li
author_sort Guimei Liu
collection DOAJ
description We consider a mapping S of the form S=α0I+α1T1+α2T2+⋯+αkTk, where αi≥0, α0>0, α1>0 and ∑i=0kαi=1. We show that the Picard iterates of S converge to a common fixed point of Ti(i=1,2,…,k)in a Banach space when Ti(i=1,2,…,k) are nonexpansive.
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issn 0161-1712
1687-0425
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publishDate 2000-01-01
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series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-eaac4857e1254bf883efef76e65ccff82025-08-20T02:22:02ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-0124317317710.1155/S0161171200003252Approximating fixed points of nonexpansive mappingsGuimei Liu0Deng Lei1Shenghong Li2Department of Mathematics, Zhejiang University, Zhejiang, 310027, ChinaDepartment of Mathematics, Southwest China Normal University, Beibei, Chongqing 400715, ChinaDepartment of Mathematics, Zhejiang University, Zhejiang, 310027, ChinaWe consider a mapping S of the form S=α0I+α1T1+α2T2+⋯+αkTk, where αi≥0, α0>0, α1>0 and ∑i=0kαi=1. We show that the Picard iterates of S converge to a common fixed point of Ti(i=1,2,…,k)in a Banach space when Ti(i=1,2,…,k) are nonexpansive.http://dx.doi.org/10.1155/S0161171200003252Fixed pointnonexpansive mappingiterative process.
spellingShingle Guimei Liu
Deng Lei
Shenghong Li
Approximating fixed points of nonexpansive mappings
International Journal of Mathematics and Mathematical Sciences
Fixed point
nonexpansive mapping
iterative process.
title Approximating fixed points of nonexpansive mappings
title_full Approximating fixed points of nonexpansive mappings
title_fullStr Approximating fixed points of nonexpansive mappings
title_full_unstemmed Approximating fixed points of nonexpansive mappings
title_short Approximating fixed points of nonexpansive mappings
title_sort approximating fixed points of nonexpansive mappings
topic Fixed point
nonexpansive mapping
iterative process.
url http://dx.doi.org/10.1155/S0161171200003252
work_keys_str_mv AT guimeiliu approximatingfixedpointsofnonexpansivemappings
AT denglei approximatingfixedpointsofnonexpansivemappings
AT shenghongli approximatingfixedpointsofnonexpansivemappings