A New Iterative Method for Finding Common Solutions of a System of Equilibrium Problems, Fixed-Point Problems, and Variational Inequalities

We introduce a new iterative scheme based on extragradient method and viscosity approximation method for finding a common element of the solutions set of a system of equilibrium problems, fixed point sets of an infinite family of nonexpansive mappings, and the solution set of a variational inequalit...

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Bibliographic Details
Published inAbstract and Applied Analysis Vol. 2010; no. 2010; pp. 990 - 1016
Main Authors Peng, Jian-Wen, Wu, Soon-Yi, Yao, Jen-Chih
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2010
Hindawi Puplishing Corporation
Hindawi Publishing Corporation
Hindawi Limited
Wiley
Subjects
Algorithms
Approximation
Convergence
Fixed points (mathematics)
Hilbert space
Inequalities
Iterative methods
Mapping
Mathematical analysis
Operations research
Optimization
Studies
Theorems
Viscosity
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Summary:We introduce a new iterative scheme based on extragradient method and viscosity approximation method for finding a common element of the solutions set of a system of equilibrium problems, fixed point sets of an infinite family of nonexpansive mappings, and the solution set of a variational inequality for a relaxed cocoercive mapping in a Hilbert space. We prove strong convergence theorem. The results in this paper unify and generalize some well-known results in the literature.
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ISSN:1085-3375
1687-0409
DOI:10.1155/2010/428293