Hybrid Iterative Scheme by a Relaxed Extragradient Method for Equilibrium Problems, a General System of Variational Inequalities and Fixed-Point Problems of a Countable Family of Nonexpansive Mappings

Based on the relaxed extragradient method and viscosity method, we introduce a new iterative method for finding a common element of solution of equilibrium problems, the solution set of a general system of variational inequalities, and the set of fixed points of a countable family of nonexpansive ma...

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Main Authors:	Qiao-Li Dong, Yan-Ni Guo, Fang Su
Format:	Article
Language:	English
Published:	Hindawi Limited 2012-01-01
Series:	Journal of Applied Mathematics
Online Access:	http://dx.doi.org/10.1155/2012/572326

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spelling	doaj-b377a63d9194406cbe7a9c552385ec9f2020-11-24T22:43:12ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/572326572326Hybrid Iterative Scheme by a Relaxed Extragradient Method for Equilibrium Problems, a General System of Variational Inequalities and Fixed-Point Problems of a Countable Family of Nonexpansive MappingsQiao-Li Dong0Yan-Ni Guo1Fang Su2College of Science, Civil Aviation University of China, Tianjin 300300, ChinaCollege of Science, Civil Aviation University of China, Tianjin 300300, ChinaCollege of Science, National University of Defense Technology, Changsha 410073, ChinaBased on the relaxed extragradient method and viscosity method, we introduce a new iterative method for finding a common element of solution of equilibrium problems, the solution set of a general system of variational inequalities, and the set of fixed points of a countable family of nonexpansive mappings in a real Hilbert space. Furthermore, we prove the strong convergence theorem of the studied iterative method. The results of this paper extend and improve the results of Ceng et al., (2008), W. Kumam and P. Kumam, (2009), Yao et al., (2010) and many others.http://dx.doi.org/10.1155/2012/572326
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Qiao-Li Dong Yan-Ni Guo Fang Su
spellingShingle	Qiao-Li Dong Yan-Ni Guo Fang Su Hybrid Iterative Scheme by a Relaxed Extragradient Method for Equilibrium Problems, a General System of Variational Inequalities and Fixed-Point Problems of a Countable Family of Nonexpansive Mappings Journal of Applied Mathematics
author_facet	Qiao-Li Dong Yan-Ni Guo Fang Su
author_sort	Qiao-Li Dong
title	Hybrid Iterative Scheme by a Relaxed Extragradient Method for Equilibrium Problems, a General System of Variational Inequalities and Fixed-Point Problems of a Countable Family of Nonexpansive Mappings
title_short	Hybrid Iterative Scheme by a Relaxed Extragradient Method for Equilibrium Problems, a General System of Variational Inequalities and Fixed-Point Problems of a Countable Family of Nonexpansive Mappings
title_full	Hybrid Iterative Scheme by a Relaxed Extragradient Method for Equilibrium Problems, a General System of Variational Inequalities and Fixed-Point Problems of a Countable Family of Nonexpansive Mappings
title_fullStr	Hybrid Iterative Scheme by a Relaxed Extragradient Method for Equilibrium Problems, a General System of Variational Inequalities and Fixed-Point Problems of a Countable Family of Nonexpansive Mappings
title_full_unstemmed	Hybrid Iterative Scheme by a Relaxed Extragradient Method for Equilibrium Problems, a General System of Variational Inequalities and Fixed-Point Problems of a Countable Family of Nonexpansive Mappings
title_sort	hybrid iterative scheme by a relaxed extragradient method for equilibrium problems, a general system of variational inequalities and fixed-point problems of a countable family of nonexpansive mappings
publisher	Hindawi Limited
series	Journal of Applied Mathematics
issn	1110-757X 1687-0042
publishDate	2012-01-01
description	Based on the relaxed extragradient method and viscosity method, we introduce a new iterative method for finding a common element of solution of equilibrium problems, the solution set of a general system of variational inequalities, and the set of fixed points of a countable family of nonexpansive mappings in a real Hilbert space. Furthermore, we prove the strong convergence theorem of the studied iterative method. The results of this paper extend and improve the results of Ceng et al., (2008), W. Kumam and P. Kumam, (2009), Yao et al., (2010) and many others.
url	http://dx.doi.org/10.1155/2012/572326
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Hybrid Iterative Scheme by a Relaxed Extragradient Method for Equilibrium Problems, a General System of Variational Inequalities and Fixed-Point Problems of a Countable Family of Nonexpansive Mappings

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