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 |
| _version_ | 1828413666167357440 |
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| author | Jung Jong Soo |
| author_facet | Jung Jong Soo |
| author_sort | Jung Jong Soo |
| collection | DOAJ |
| description | <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> |
| first_indexed | 2024-12-10T13:13:10Z |
| format | Article |
| id | doaj.art-6768989c0bfc4aac8d70563a2443e89d |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-12-10T13:13:10Z |
| publishDate | 2011-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-6768989c0bfc4aac8d70563a2443e89d2022-12-22T01:47:37ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2011-01-012011151A general composite iterative method for generalized mixed equilibrium problems, variational inequality problems and optimization problemsJung Jong Soo<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>http://www.journalofinequalitiesandapplications.com/content/2011/1/51generalized mixed equilibrium problemfixed pointnonexpansive mapping; inverse-strongly monotone mappingvariational inequality; optimization problemmetric projectionstrongly positive bounded linear operator |
| spellingShingle | Jung Jong Soo A general composite iterative method for generalized mixed equilibrium problems, variational inequality problems and optimization problems Journal of Inequalities and Applications generalized mixed equilibrium problem fixed point nonexpansive mapping; inverse-strongly monotone mapping variational inequality; optimization problem metric projection strongly positive bounded linear operator |
| title | A general composite iterative method for generalized mixed equilibrium problems, variational inequality problems and optimization problems |
| title_full | A general composite iterative method for generalized mixed equilibrium problems, variational inequality problems and optimization problems |
| title_fullStr | A general composite iterative method for generalized mixed equilibrium problems, variational inequality problems and optimization problems |
| title_full_unstemmed | A general composite iterative method for generalized mixed equilibrium problems, variational inequality problems and optimization problems |
| title_short | A general composite iterative method for generalized mixed equilibrium problems, variational inequality problems and optimization problems |
| title_sort | general composite iterative method for generalized mixed equilibrium problems variational inequality problems and optimization problems |
| topic | generalized mixed equilibrium problem fixed point nonexpansive mapping; inverse-strongly monotone mapping variational inequality; optimization problem metric projection strongly positive bounded linear operator |
| url | http://www.journalofinequalitiesandapplications.com/content/2011/1/51 |
| work_keys_str_mv | AT jungjongsoo ageneralcompositeiterativemethodforgeneralizedmixedequilibriumproblemsvariationalinequalityproblemsandoptimizationproblems AT jungjongsoo generalcompositeiterativemethodforgeneralizedmixedequilibriumproblemsvariationalinequalityproblemsandoptimizationproblems |