New Generalized Mixed Equilibrium Problem with Respect to Relaxed Semi-Monotone Mappings in Banach Spaces
We introduce the new generalized mixed equilibrium problem with respect to relaxed semimonotone mappings. Using the KKM technique, we obtain the existence of solutions for the generalized mixed equilibrium problem in Banach spaces. Furthermore, we also introduce a hybrid projection algorithm for fin...
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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/10.1155/2012/790592 |
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| _version_ | 1832567317202993152 |
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| author | Rabian Wangkeeree Pakkapon Preechasilp |
| author_facet | Rabian Wangkeeree Pakkapon Preechasilp |
| author_sort | Rabian Wangkeeree |
| collection | DOAJ |
| description | We introduce the new generalized mixed equilibrium problem with respect to relaxed semimonotone
mappings. Using the KKM technique, we obtain the existence of solutions for the generalized mixed equilibrium
problem in Banach spaces. Furthermore, we also introduce a hybrid projection algorithm for finding a common element
in the solution set of a generalized mixed equilibrium problem and the fixed point set of an asymptotically nonexpansive
mapping. The strong convergence theorem of the proposed sequence is obtained in a Banach space setting. The main
results extend various results existing in the current literature. |
| format | Article |
| id | doaj-art-7bf8126cc0314703bd7740b00d6016a5 |
| 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-7bf8126cc0314703bd7740b00d6016a52025-02-03T01:01:48ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/790592790592New Generalized Mixed Equilibrium Problem with Respect to Relaxed Semi-Monotone Mappings in Banach SpacesRabian Wangkeeree0Pakkapon Preechasilp1Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandDepartment of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandWe introduce the new generalized mixed equilibrium problem with respect to relaxed semimonotone mappings. Using the KKM technique, we obtain the existence of solutions for the generalized mixed equilibrium problem in Banach spaces. Furthermore, we also introduce a hybrid projection algorithm for finding a common element in the solution set of a generalized mixed equilibrium problem and the fixed point set of an asymptotically nonexpansive mapping. The strong convergence theorem of the proposed sequence is obtained in a Banach space setting. The main results extend various results existing in the current literature.http://dx.doi.org/10.1155/2012/790592 |
| spellingShingle | Rabian Wangkeeree Pakkapon Preechasilp New Generalized Mixed Equilibrium Problem with Respect to Relaxed Semi-Monotone Mappings in Banach Spaces Journal of Applied Mathematics |
| title | New Generalized Mixed Equilibrium Problem with Respect to Relaxed Semi-Monotone Mappings in Banach Spaces |
| title_full | New Generalized Mixed Equilibrium Problem with Respect to Relaxed Semi-Monotone Mappings in Banach Spaces |
| title_fullStr | New Generalized Mixed Equilibrium Problem with Respect to Relaxed Semi-Monotone Mappings in Banach Spaces |
| title_full_unstemmed | New Generalized Mixed Equilibrium Problem with Respect to Relaxed Semi-Monotone Mappings in Banach Spaces |
| title_short | New Generalized Mixed Equilibrium Problem with Respect to Relaxed Semi-Monotone Mappings in Banach Spaces |
| title_sort | new generalized mixed equilibrium problem with respect to relaxed semi monotone mappings in banach spaces |
| url | http://dx.doi.org/10.1155/2012/790592 |
| work_keys_str_mv | AT rabianwangkeeree newgeneralizedmixedequilibriumproblemwithrespecttorelaxedsemimonotonemappingsinbanachspaces AT pakkaponpreechasilp newgeneralizedmixedequilibriumproblemwithrespecttorelaxedsemimonotonemappingsinbanachspaces |