A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone Operators
We introduce a new hybrid iterative scheme for finding a common element of the set of common fixed points of two countable families of relatively quasi-nonexpansive mappings, the set of the variational inequality, the set of solutions of the generalized mixed equilibrium problem, and zeros of maxima...
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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/10.1155/2012/712651 |
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| _version_ | 1850208853585559552 |
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| author | Yaqin Wang |
| author_facet | Yaqin Wang |
| author_sort | Yaqin Wang |
| collection | DOAJ |
| description | We introduce a new hybrid iterative scheme for finding a common element of the set of common fixed points of two countable families of relatively quasi-nonexpansive mappings, the set of the variational inequality, the set of solutions of the generalized mixed equilibrium problem, and zeros of maximal monotone operators in a Banach space. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. The results obtained in this paper improve and extend the result of Zeng et al. (2010) and many others. |
| format | Article |
| id | doaj-art-91a7209cd74e49a68849340f4041f269 |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-91a7209cd74e49a68849340f4041f2692025-08-20T02:10:09ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/712651712651A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone OperatorsYaqin Wang0Mathematical College, Sichuan University, Chengdu, Sichuan 610064, ChinaWe introduce a new hybrid iterative scheme for finding a common element of the set of common fixed points of two countable families of relatively quasi-nonexpansive mappings, the set of the variational inequality, the set of solutions of the generalized mixed equilibrium problem, and zeros of maximal monotone operators in a Banach space. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. The results obtained in this paper improve and extend the result of Zeng et al. (2010) and many others.http://dx.doi.org/10.1155/2012/712651 |
| spellingShingle | Yaqin Wang A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone Operators Journal of Applied Mathematics |
| title | A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone Operators |
| title_full | A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone Operators |
| title_fullStr | A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone Operators |
| title_full_unstemmed | A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone Operators |
| title_short | A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone Operators |
| title_sort | new hybrid method for equilibrium problems variational inequality problems fixed point problems and zero of maximal monotone operators |
| url | http://dx.doi.org/10.1155/2012/712651 |
| work_keys_str_mv | AT yaqinwang anewhybridmethodforequilibriumproblemsvariationalinequalityproblemsfixedpointproblemsandzeroofmaximalmonotoneoperators AT yaqinwang newhybridmethodforequilibriumproblemsvariationalinequalityproblemsfixedpointproblemsandzeroofmaximalmonotoneoperators |