Convergence Analysis for a System of Equilibrium Problems and a Countable Family of Relatively Quasi-Nonexpansive Mappings in Banach Spaces
We introduce a new hybrid iterative scheme for finding a common element in the solutions set of a system of equilibrium problems and the common fixed points set of an infinitely countable family of relatively quasi-nonexpansive map...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/141376 |
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| _version_ | 1832567192472780800 |
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| author | Prasit Cholamjiak Suthep Suantai |
| author_facet | Prasit Cholamjiak Suthep Suantai |
| author_sort | Prasit Cholamjiak |
| collection | DOAJ |
| description | We introduce a new hybrid iterative scheme for
finding a common element in the solutions set of a
system of equilibrium problems and the common
fixed points set of an infinitely countable family
of relatively quasi-nonexpansive
mappings in the framework of Banach spaces. We prove the strong convergence theorem by the shrinking projection method. In addition, the results obtained in this paper can be applied to a system of variational inequality problems and to a system of convex minimization problems in a Banach space. |
| format | Article |
| id | doaj-art-becfd38fdca3415ca536d41075ec8fe8 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-becfd38fdca3415ca536d41075ec8fe82025-02-03T01:02:10ZengWileyAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/141376141376Convergence Analysis for a System of Equilibrium Problems and a Countable Family of Relatively Quasi-Nonexpansive Mappings in Banach SpacesPrasit Cholamjiak0Suthep Suantai1Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandDepartment of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandWe introduce a new hybrid iterative scheme for finding a common element in the solutions set of a system of equilibrium problems and the common fixed points set of an infinitely countable family of relatively quasi-nonexpansive mappings in the framework of Banach spaces. We prove the strong convergence theorem by the shrinking projection method. In addition, the results obtained in this paper can be applied to a system of variational inequality problems and to a system of convex minimization problems in a Banach space.http://dx.doi.org/10.1155/2010/141376 |
| spellingShingle | Prasit Cholamjiak Suthep Suantai Convergence Analysis for a System of Equilibrium Problems and a Countable Family of Relatively Quasi-Nonexpansive Mappings in Banach Spaces Abstract and Applied Analysis |
| title | Convergence Analysis for a System of Equilibrium Problems and a Countable Family of Relatively Quasi-Nonexpansive Mappings in Banach Spaces |
| title_full | Convergence Analysis for a System of Equilibrium Problems and a Countable Family of Relatively Quasi-Nonexpansive Mappings in Banach Spaces |
| title_fullStr | Convergence Analysis for a System of Equilibrium Problems and a Countable Family of Relatively Quasi-Nonexpansive Mappings in Banach Spaces |
| title_full_unstemmed | Convergence Analysis for a System of Equilibrium Problems and a Countable Family of Relatively Quasi-Nonexpansive Mappings in Banach Spaces |
| title_short | Convergence Analysis for a System of Equilibrium Problems and a Countable Family of Relatively Quasi-Nonexpansive Mappings in Banach Spaces |
| title_sort | convergence analysis for a system of equilibrium problems and a countable family of relatively quasi nonexpansive mappings in banach spaces |
| url | http://dx.doi.org/10.1155/2010/141376 |
| work_keys_str_mv | AT prasitcholamjiak convergenceanalysisforasystemofequilibriumproblemsandacountablefamilyofrelativelyquasinonexpansivemappingsinbanachspaces AT suthepsuantai convergenceanalysisforasystemofequilibriumproblemsandacountablefamilyofrelativelyquasinonexpansivemappingsinbanachspaces |