A New Iterative Scheme for Generalized Mixed Equilibrium, Variational Inequality Problems, and a Zero Point of Maximal Monotone Operators
The purpose of this paper is to introduce a new iterative scheme for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of solutions of variational inequality problems, the zero point of maximal monotone operators, and the set of two countable familie...
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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/10.1155/2012/692829 |
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| _version_ | 1832545742855602176 |
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| author | Kriengsak Wattanawitoon Poom Kumam |
| author_facet | Kriengsak Wattanawitoon Poom Kumam |
| author_sort | Kriengsak Wattanawitoon |
| collection | DOAJ |
| description | The purpose of this paper is to introduce a new iterative scheme for finding a common
element of the set of solutions of generalized mixed equilibrium problems, the set of solutions of
variational inequality problems, the zero point of maximal monotone operators, and the set of two
countable families of quasi-ϕ-nonexpansive mappings in Banach spaces. Moreover, the strong convergence
theorems of this method are established under the suitable conditions of the parameter imposed
on the algorithm. Finally, we apply our results to finding a zero point of inverse-strongly monotone
operators and complementarity problems. Our results presented in this paper improve and extend
the recently results by many others. |
| format | Article |
| id | doaj-art-d5807fd20c2a42be8b5d8e58302e9123 |
| 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-d5807fd20c2a42be8b5d8e58302e91232025-02-03T07:24:59ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/692829692829A New Iterative Scheme for Generalized Mixed Equilibrium, Variational Inequality Problems, and a Zero Point of Maximal Monotone OperatorsKriengsak Wattanawitoon0Poom Kumam1Department of Mathematics and Statistics, Faculty of Science and Agricultural Technology, Rajamangala University of Technology Lanna Tak, Tak 63000, ThailandDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangmod, Thungkru, Bangkok 10140, ThailandThe purpose of this paper is to introduce a new iterative scheme for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of solutions of variational inequality problems, the zero point of maximal monotone operators, and the set of two countable families of quasi-ϕ-nonexpansive mappings in Banach spaces. Moreover, the strong convergence theorems of this method are established under the suitable conditions of the parameter imposed on the algorithm. Finally, we apply our results to finding a zero point of inverse-strongly monotone operators and complementarity problems. Our results presented in this paper improve and extend the recently results by many others.http://dx.doi.org/10.1155/2012/692829 |
| spellingShingle | Kriengsak Wattanawitoon Poom Kumam A New Iterative Scheme for Generalized Mixed Equilibrium, Variational Inequality Problems, and a Zero Point of Maximal Monotone Operators Journal of Applied Mathematics |
| title | A New Iterative Scheme for Generalized Mixed Equilibrium, Variational Inequality Problems, and a Zero Point of Maximal Monotone Operators |
| title_full | A New Iterative Scheme for Generalized Mixed Equilibrium, Variational Inequality Problems, and a Zero Point of Maximal Monotone Operators |
| title_fullStr | A New Iterative Scheme for Generalized Mixed Equilibrium, Variational Inequality Problems, and a Zero Point of Maximal Monotone Operators |
| title_full_unstemmed | A New Iterative Scheme for Generalized Mixed Equilibrium, Variational Inequality Problems, and a Zero Point of Maximal Monotone Operators |
| title_short | A New Iterative Scheme for Generalized Mixed Equilibrium, Variational Inequality Problems, and a Zero Point of Maximal Monotone Operators |
| title_sort | new iterative scheme for generalized mixed equilibrium variational inequality problems and a zero point of maximal monotone operators |
| url | http://dx.doi.org/10.1155/2012/692829 |
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