A Hybrid Extragradient-Like Method for Variational Inequalities, Equilibrium Problems, and an Infinitely Family of Strictly Pseudocontractive Mappings

The purpose of this paper is to consider a new scheme by the hybrid extragradient-like method for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of solutions of a variational inequality, and the set of fixed points of an infinitely family of stri...

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Bibliographic Details
Published inJournal of Applied Mathematics Vol. 2012; no. 2012; pp. 1007 - 1021-660
Main Authors Wang, Yaqin, Fang, Xiaoli, Xu, Hong Kun
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2012
Hindawi Publishing Corporation
Hindawi Limited
Wiley
Subjects
Convergence
Hilbert space
Inequalities
Inequality
Iterative algorithms
Iterative methods
Mapping
Mathematical analysis
Methods
Optimization
Studies
Theorems
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Summary:The purpose of this paper is to consider a new scheme by the hybrid extragradient-like method for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of solutions of a variational inequality, and the set of fixed points of an infinitely family of strictly pseudocontractive mappings in Hilbert spaces. Then, we obtain a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm. Our results extend and improve the results of Issara Inchan (2010) and many others.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:1110-757X
1687-0042
DOI:10.1155/2012/804642