Convergence Theorems for Maximal Monotone Operators, Weak Relatively Nonexpansive Mappings and Equilibrium Problems
We introduce hybrid-iterative schemes for solving a system of the zero-finding problems of maximal monotone operators, the equilibrium problem, and the fixed point problem of weak relatively nonexpansive mappings. We then prove, in a uniformly smooth and uniformly convex Banach space, strong converg...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/804538 |
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| author | Kamonrat Nammanee Suthep Suantai Prasit Cholamjiak |
| author_facet | Kamonrat Nammanee Suthep Suantai Prasit Cholamjiak |
| author_sort | Kamonrat Nammanee |
| collection | DOAJ |
| description | We introduce hybrid-iterative schemes for solving a system of the zero-finding problems of maximal monotone operators, the equilibrium problem, and the fixed point problem of weak relatively nonexpansive mappings. We then prove, in a uniformly smooth and uniformly convex Banach space, strong convergence theorems by using a shrinking projection method. We finally apply the obtained results to a system of convex minimization problems. |
| format | Article |
| id | doaj-art-786eb8f3b38140739f967a2620c070a5 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-786eb8f3b38140739f967a2620c070a52025-02-03T01:27:50ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/804538804538Convergence Theorems for Maximal Monotone Operators, Weak Relatively Nonexpansive Mappings and Equilibrium ProblemsKamonrat Nammanee0Suthep Suantai1Prasit Cholamjiak2School of Science, University of Phayao, Phayao 56000, ThailandDepartment of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandSchool of Science, University of Phayao, Phayao 56000, ThailandWe introduce hybrid-iterative schemes for solving a system of the zero-finding problems of maximal monotone operators, the equilibrium problem, and the fixed point problem of weak relatively nonexpansive mappings. We then prove, in a uniformly smooth and uniformly convex Banach space, strong convergence theorems by using a shrinking projection method. We finally apply the obtained results to a system of convex minimization problems.http://dx.doi.org/10.1155/2012/804538 |
| spellingShingle | Kamonrat Nammanee Suthep Suantai Prasit Cholamjiak Convergence Theorems for Maximal Monotone Operators, Weak Relatively Nonexpansive Mappings and Equilibrium Problems Journal of Applied Mathematics |
| title | Convergence Theorems for Maximal Monotone Operators, Weak Relatively Nonexpansive Mappings and Equilibrium Problems |
| title_full | Convergence Theorems for Maximal Monotone Operators, Weak Relatively Nonexpansive Mappings and Equilibrium Problems |
| title_fullStr | Convergence Theorems for Maximal Monotone Operators, Weak Relatively Nonexpansive Mappings and Equilibrium Problems |
| title_full_unstemmed | Convergence Theorems for Maximal Monotone Operators, Weak Relatively Nonexpansive Mappings and Equilibrium Problems |
| title_short | Convergence Theorems for Maximal Monotone Operators, Weak Relatively Nonexpansive Mappings and Equilibrium Problems |
| title_sort | convergence theorems for maximal monotone operators weak relatively nonexpansive mappings and equilibrium problems |
| url | http://dx.doi.org/10.1155/2012/804538 |
| work_keys_str_mv | AT kamonratnammanee convergencetheoremsformaximalmonotoneoperatorsweakrelativelynonexpansivemappingsandequilibriumproblems AT suthepsuantai convergencetheoremsformaximalmonotoneoperatorsweakrelativelynonexpansivemappingsandequilibriumproblems AT prasitcholamjiak convergencetheoremsformaximalmonotoneoperatorsweakrelativelynonexpansivemappingsandequilibriumproblems |