Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space

We introduce a hybrid iterative scheme for finding a common element of the set of common fixed points for a family of infinitely nonexpansive mappings, the set of solutions of the varitional inequality problem and the equilibrium problem in Hilbert space. Under suitable conditions, some strong conve...

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Main Authors: Zhou Yinying, Cao Jiantao, Wang Yali
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2014/232541
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author Zhou Yinying
Cao Jiantao
Wang Yali
author_facet Zhou Yinying
Cao Jiantao
Wang Yali
author_sort Zhou Yinying
collection DOAJ
description We introduce a hybrid iterative scheme for finding a common element of the set of common fixed points for a family of infinitely nonexpansive mappings, the set of solutions of the varitional inequality problem and the equilibrium problem in Hilbert space. Under suitable conditions, some strong convergence theorems are obtained. Our results improve and extend the corresponding results in (Chang et al. (2009), Min and Chang (2012), Plubtieng and Punpaeng (2007), S. Takahashi and W. Takahashi (2007), Tada and Takahashi (2007), Gang and Changsong (2009), Ying (2013), Y. Yao and J. C. Yao (2007), and Yong-Cho and Kang (2012)).
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publishDate 2014-01-01
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series Journal of Applied Mathematics
spelling doaj-art-ba4be05b43d44303a6d9a0ff1a1dc0e82025-02-03T05:52:21ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/232541232541Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert SpaceZhou Yinying0Cao Jiantao1Wang Yali2Department of Mathematics and Information Sciences, Langfang Teachers College, Langfang, Hebei 065000, ChinaDepartment of Mathematics and Information Sciences, Langfang Teachers College, Langfang, Hebei 065000, ChinaDepartment of Mathematics and Information Sciences, Langfang Teachers College, Langfang, Hebei 065000, ChinaWe introduce a hybrid iterative scheme for finding a common element of the set of common fixed points for a family of infinitely nonexpansive mappings, the set of solutions of the varitional inequality problem and the equilibrium problem in Hilbert space. Under suitable conditions, some strong convergence theorems are obtained. Our results improve and extend the corresponding results in (Chang et al. (2009), Min and Chang (2012), Plubtieng and Punpaeng (2007), S. Takahashi and W. Takahashi (2007), Tada and Takahashi (2007), Gang and Changsong (2009), Ying (2013), Y. Yao and J. C. Yao (2007), and Yong-Cho and Kang (2012)).http://dx.doi.org/10.1155/2014/232541
spellingShingle Zhou Yinying
Cao Jiantao
Wang Yali
Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space
Journal of Applied Mathematics
title Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space
title_full Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space
title_fullStr Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space
title_full_unstemmed Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space
title_short Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space
title_sort convergence theorem for equilibrium and variational inequality problems and a family of infinitely nonexpansive mappings in hilbert space
url http://dx.doi.org/10.1155/2014/232541
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AT wangyali convergencetheoremforequilibriumandvariationalinequalityproblemsandafamilyofinfinitelynonexpansivemappingsinhilbertspace