Existence and Iterative Approximation Methods for Generalized Mixed Vector Equilibrium Problems with Relaxed Monotone Mappings
We first consider an auxiliary problem for the generalized mixed vector equilibrium problem with a relaxed monotone mapping and prove the existence and uniqueness of the solution for the auxiliary problem. We then introduce a new iterative scheme for approximating a common element of the set of solu...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/973408 |
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| _version_ | 1832549348266737664 |
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| author | Rabian Wangkeeree Panu Yimmuang |
| author_facet | Rabian Wangkeeree Panu Yimmuang |
| author_sort | Rabian Wangkeeree |
| collection | DOAJ |
| description | We first consider an auxiliary problem for the generalized mixed vector equilibrium problem with a relaxed monotone mapping and prove the existence and uniqueness of the solution for the auxiliary problem. We then introduce a new iterative scheme for approximating a common element of the set of solutions of a generalized mixed vector equilibrium problem with a relaxed monotone mapping and the set of common fixed points of a countable family of nonexpansive mappings. The results presented in this paper can be considered as a generalization of some known results due to Wang et al. (2010). |
| format | Article |
| id | doaj-art-fc58c42d8135452bbc5b0b78c7bd97a2 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-fc58c42d8135452bbc5b0b78c7bd97a22025-02-03T06:11:41ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/973408973408Existence and Iterative Approximation Methods for Generalized Mixed Vector Equilibrium Problems with Relaxed Monotone MappingsRabian Wangkeeree0Panu Yimmuang1Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandDepartment of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandWe first consider an auxiliary problem for the generalized mixed vector equilibrium problem with a relaxed monotone mapping and prove the existence and uniqueness of the solution for the auxiliary problem. We then introduce a new iterative scheme for approximating a common element of the set of solutions of a generalized mixed vector equilibrium problem with a relaxed monotone mapping and the set of common fixed points of a countable family of nonexpansive mappings. The results presented in this paper can be considered as a generalization of some known results due to Wang et al. (2010).http://dx.doi.org/10.1155/2013/973408 |
| spellingShingle | Rabian Wangkeeree Panu Yimmuang Existence and Iterative Approximation Methods for Generalized Mixed Vector Equilibrium Problems with Relaxed Monotone Mappings Journal of Applied Mathematics |
| title | Existence and Iterative Approximation Methods for Generalized Mixed Vector Equilibrium Problems with Relaxed Monotone Mappings |
| title_full | Existence and Iterative Approximation Methods for Generalized Mixed Vector Equilibrium Problems with Relaxed Monotone Mappings |
| title_fullStr | Existence and Iterative Approximation Methods for Generalized Mixed Vector Equilibrium Problems with Relaxed Monotone Mappings |
| title_full_unstemmed | Existence and Iterative Approximation Methods for Generalized Mixed Vector Equilibrium Problems with Relaxed Monotone Mappings |
| title_short | Existence and Iterative Approximation Methods for Generalized Mixed Vector Equilibrium Problems with Relaxed Monotone Mappings |
| title_sort | existence and iterative approximation methods for generalized mixed vector equilibrium problems with relaxed monotone mappings |
| url | http://dx.doi.org/10.1155/2013/973408 |
| work_keys_str_mv | AT rabianwangkeeree existenceanditerativeapproximationmethodsforgeneralizedmixedvectorequilibriumproblemswithrelaxedmonotonemappings AT panuyimmuang existenceanditerativeapproximationmethodsforgeneralizedmixedvectorequilibriumproblemswithrelaxedmonotonemappings |