A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces
We introduce a new general system of variational inclusions in Banach spaces and propose a new iterative scheme for finding common element of the set of solutions of the variational inclusion with set-valued maximal monotone mapping and Lipschitzian relaxed cocoercive mapping and the set of fixed po...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/187052 |
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| _version_ | 1832545376743194624 |
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| author | Pongsakorn Sunthrayuth Poom Kumam |
| author_facet | Pongsakorn Sunthrayuth Poom Kumam |
| author_sort | Pongsakorn Sunthrayuth |
| collection | DOAJ |
| description | We introduce a new general system of variational inclusions in Banach spaces and propose a new iterative scheme for finding common element of the set of solutions of the variational inclusion with set-valued maximal monotone mapping and Lipschitzian relaxed cocoercive mapping and the set of fixed point of nonexpansive semigroups in a uniformly convex and 2-uniformly smooth Banach space. Furthermore, strong convergence theorems are established under some certain control conditions. As applications, finding a common solution for a system of variational inequality problems and minimization problems is given. |
| format | Article |
| id | doaj-art-77485454a94548cf9f4215c82d351606 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-77485454a94548cf9f4215c82d3516062025-02-03T07:26:03ZengWileyJournal of Applied Mathematics1110-757X1687-00422011-01-01201110.1155/2011/187052187052A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach SpacesPongsakorn Sunthrayuth0Poom Kumam1Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangmod, Bangkok 10140, ThailandDepartment of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangmod, Bangkok 10140, ThailandWe introduce a new general system of variational inclusions in Banach spaces and propose a new iterative scheme for finding common element of the set of solutions of the variational inclusion with set-valued maximal monotone mapping and Lipschitzian relaxed cocoercive mapping and the set of fixed point of nonexpansive semigroups in a uniformly convex and 2-uniformly smooth Banach space. Furthermore, strong convergence theorems are established under some certain control conditions. As applications, finding a common solution for a system of variational inequality problems and minimization problems is given.http://dx.doi.org/10.1155/2011/187052 |
| spellingShingle | Pongsakorn Sunthrayuth Poom Kumam A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces Journal of Applied Mathematics |
| title | A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces |
| title_full | A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces |
| title_fullStr | A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces |
| title_full_unstemmed | A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces |
| title_short | A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces |
| title_sort | new general iterative method for solution of a new general system of variational inclusions for nonexpansive semigroups in banach spaces |
| url | http://dx.doi.org/10.1155/2011/187052 |
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