Shrinking Projection Method of Common Solutions for Generalized Equilibrium Quasi-<inline-formula> <graphic file="1029-242X-2010-101690-i1.gif"/></inline-formula>-Nonexpansive Mapping and Relatively Nonexpansive Mapping

Shrinking Projection Method of Common Solutions for Generalized Equilibrium Quasi-<inline-formula> <graphic file="1029-242X-2010-101690-i1.gif"/></inline-formula>-Nonexpansive Mapping and Relatively Nonexpansive Mapping

<p/> <p>We prove a strong convergence theorem for finding a common element of the set of solutions for generalized equilibrium problems, the set of fixed points of a relatively nonexpansive mapping, and the set of fixed points of a quasi-<inline-formula> <graphic file="1029...

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Main Authors: Liu Min, Chang Shih-Sen, Zuo Ping
Format: Article
Language:English
Published: SpringerOpen 2010-01-01
Series:Journal of Inequalities and Applications
Online Access:http://www.journalofinequalitiesandapplications.com/content/2010/101690
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spelling doaj-d5ecd118cc32426b8951176a8b0845c02020-11-24T21:33:53ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2010-01-0120101101690Shrinking Projection Method of Common Solutions for Generalized Equilibrium Quasi-<inline-formula> <graphic file="1029-242X-2010-101690-i1.gif"/></inline-formula>-Nonexpansive Mapping and Relatively Nonexpansive MappingLiu MinChang Shih-SenZuo Ping<p/> <p>We prove a strong convergence theorem for finding a common element of the set of solutions for generalized equilibrium problems, the set of fixed points of a relatively nonexpansive mapping, and the set of fixed points of a quasi-<inline-formula> <graphic file="1029-242X-2010-101690-i2.gif"/></inline-formula>-nonexpansive mapping in a Banach space by using the shrinking Projection method. Our results improve the main results in S. Takahashi and W. Takahashi (2008) and Takahashi and Zembayashi (2008). Moreover, the method of proof adopted in the paper is different from that of S. Takahashi and W. Zembayashi (2008).</p>http://www.journalofinequalitiesandapplications.com/content/2010/101690
collection DOAJ
language English
format Article
sources DOAJ
author Liu Min
Chang Shih-Sen
Zuo Ping
spellingShingle Liu Min
Chang Shih-Sen
Zuo Ping
Shrinking Projection Method of Common Solutions for Generalized Equilibrium Quasi-<inline-formula> <graphic file="1029-242X-2010-101690-i1.gif"/></inline-formula>-Nonexpansive Mapping and Relatively Nonexpansive Mapping
Journal of Inequalities and Applications
author_facet Liu Min
Chang Shih-Sen
Zuo Ping
author_sort Liu Min
title Shrinking Projection Method of Common Solutions for Generalized Equilibrium Quasi-<inline-formula> <graphic file="1029-242X-2010-101690-i1.gif"/></inline-formula>-Nonexpansive Mapping and Relatively Nonexpansive Mapping
title_short Shrinking Projection Method of Common Solutions for Generalized Equilibrium Quasi-<inline-formula> <graphic file="1029-242X-2010-101690-i1.gif"/></inline-formula>-Nonexpansive Mapping and Relatively Nonexpansive Mapping
title_full Shrinking Projection Method of Common Solutions for Generalized Equilibrium Quasi-<inline-formula> <graphic file="1029-242X-2010-101690-i1.gif"/></inline-formula>-Nonexpansive Mapping and Relatively Nonexpansive Mapping
title_fullStr Shrinking Projection Method of Common Solutions for Generalized Equilibrium Quasi-<inline-formula> <graphic file="1029-242X-2010-101690-i1.gif"/></inline-formula>-Nonexpansive Mapping and Relatively Nonexpansive Mapping
title_full_unstemmed Shrinking Projection Method of Common Solutions for Generalized Equilibrium Quasi-<inline-formula> <graphic file="1029-242X-2010-101690-i1.gif"/></inline-formula>-Nonexpansive Mapping and Relatively Nonexpansive Mapping
title_sort shrinking projection method of common solutions for generalized equilibrium quasi-<inline-formula> <graphic file="1029-242x-2010-101690-i1.gif"/></inline-formula>-nonexpansive mapping and relatively nonexpansive mapping
publisher SpringerOpen
series Journal of Inequalities and Applications
issn 1025-5834
1029-242X
publishDate 2010-01-01
description <p/> <p>We prove a strong convergence theorem for finding a common element of the set of solutions for generalized equilibrium problems, the set of fixed points of a relatively nonexpansive mapping, and the set of fixed points of a quasi-<inline-formula> <graphic file="1029-242X-2010-101690-i2.gif"/></inline-formula>-nonexpansive mapping in a Banach space by using the shrinking Projection method. Our results improve the main results in S. Takahashi and W. Takahashi (2008) and Takahashi and Zembayashi (2008). Moreover, the method of proof adopted in the paper is different from that of S. Takahashi and W. Zembayashi (2008).</p>
url http://www.journalofinequalitiesandapplications.com/content/2010/101690
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AT changshihsen shrinkingprojectionmethodofcommonsolutionsforgeneralizedequilibriumquasiinlineformulagraphicfile1029242x2010101690i1gifinlineformulanonexpansivemappingandrelativelynonexpansivemapping
AT zuoping shrinkingprojectionmethodofcommonsolutionsforgeneralizedequilibriumquasiinlineformulagraphicfile1029242x2010101690i1gifinlineformulanonexpansivemappingandrelativelynonexpansivemapping
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