A general composite iterative method for generalized mixed equilibrium problems, variational inequality problems and optimization problems
<p>Abstract</p> <p>In this article, we introduce a new general composite iterative scheme for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2011-01-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2011/1/51 |
| Summary: | <p>Abstract</p> <p>In this article, we introduce a new general composite iterative scheme for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality problem for an inverse-strongly monotone mapping in Hilbert spaces. It is shown that the sequence generated by the proposed iterative scheme converges strongly to a common element of the above three sets under suitable control conditions, which solves a certain optimization problem. The results of this article substantially improve, develop, and complement the previous well-known results in this area.</p> <p> <b>2010 Mathematics Subject Classifications: </b>49J30; 49J40; 47H09; 47H10; 47J20; 47J25; 47J05; 49M05.</p> |
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| ISSN: | 1025-5834 1029-242X |