Hybrid Iterative Scheme by a Relaxed Extragradient Method for Equilibrium Problems, a General System of Variational Inequalities and Fixed-Point Problems of a Countable Family of Nonexpansive Mappings
Based on the relaxed extragradient method and viscosity method, we introduce a new iterative method for finding a common element of solution of equilibrium problems, the solution set of a general system of variational inequalities, and the set of fixed points of a countable family of nonexpansive ma...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/572326 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832565122870018048 |
|---|---|
| author | Qiao-Li Dong Yan-Ni Guo Fang Su |
| author_facet | Qiao-Li Dong Yan-Ni Guo Fang Su |
| author_sort | Qiao-Li Dong |
| collection | DOAJ |
| description | Based on the relaxed extragradient method and viscosity method, we introduce a new iterative method for finding a common element of solution of equilibrium problems, the solution set of a general system of variational inequalities, and the set of fixed points of a countable family of nonexpansive mappings in a real Hilbert space. Furthermore, we prove the strong convergence theorem of the studied iterative method. The results of this paper extend and improve the results of Ceng et al., (2008), W. Kumam and P. Kumam, (2009), Yao et al., (2010) and many others. |
| format | Article |
| id | doaj-art-b377a63d9194406cbe7a9c552385ec9f |
| 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-b377a63d9194406cbe7a9c552385ec9f2025-02-03T01:09:30ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/572326572326Hybrid Iterative Scheme by a Relaxed Extragradient Method for Equilibrium Problems, a General System of Variational Inequalities and Fixed-Point Problems of a Countable Family of Nonexpansive MappingsQiao-Li Dong0Yan-Ni Guo1Fang Su2College of Science, Civil Aviation University of China, Tianjin 300300, ChinaCollege of Science, Civil Aviation University of China, Tianjin 300300, ChinaCollege of Science, National University of Defense Technology, Changsha 410073, ChinaBased on the relaxed extragradient method and viscosity method, we introduce a new iterative method for finding a common element of solution of equilibrium problems, the solution set of a general system of variational inequalities, and the set of fixed points of a countable family of nonexpansive mappings in a real Hilbert space. Furthermore, we prove the strong convergence theorem of the studied iterative method. The results of this paper extend and improve the results of Ceng et al., (2008), W. Kumam and P. Kumam, (2009), Yao et al., (2010) and many others.http://dx.doi.org/10.1155/2012/572326 |
| spellingShingle | Qiao-Li Dong Yan-Ni Guo Fang Su Hybrid Iterative Scheme by a Relaxed Extragradient Method for Equilibrium Problems, a General System of Variational Inequalities and Fixed-Point Problems of a Countable Family of Nonexpansive Mappings Journal of Applied Mathematics |
| title | Hybrid Iterative Scheme by a Relaxed Extragradient Method for Equilibrium Problems, a General System of Variational Inequalities and Fixed-Point Problems of a Countable Family of Nonexpansive Mappings |
| title_full | Hybrid Iterative Scheme by a Relaxed Extragradient Method for Equilibrium Problems, a General System of Variational Inequalities and Fixed-Point Problems of a Countable Family of Nonexpansive Mappings |
| title_fullStr | Hybrid Iterative Scheme by a Relaxed Extragradient Method for Equilibrium Problems, a General System of Variational Inequalities and Fixed-Point Problems of a Countable Family of Nonexpansive Mappings |
| title_full_unstemmed | Hybrid Iterative Scheme by a Relaxed Extragradient Method for Equilibrium Problems, a General System of Variational Inequalities and Fixed-Point Problems of a Countable Family of Nonexpansive Mappings |
| title_short | Hybrid Iterative Scheme by a Relaxed Extragradient Method for Equilibrium Problems, a General System of Variational Inequalities and Fixed-Point Problems of a Countable Family of Nonexpansive Mappings |
| title_sort | hybrid iterative scheme by a relaxed extragradient method for equilibrium problems a general system of variational inequalities and fixed point problems of a countable family of nonexpansive mappings |
| url | http://dx.doi.org/10.1155/2012/572326 |
| work_keys_str_mv | AT qiaolidong hybriditerativeschemebyarelaxedextragradientmethodforequilibriumproblemsageneralsystemofvariationalinequalitiesandfixedpointproblemsofacountablefamilyofnonexpansivemappings AT yanniguo hybriditerativeschemebyarelaxedextragradientmethodforequilibriumproblemsageneralsystemofvariationalinequalitiesandfixedpointproblemsofacountablefamilyofnonexpansivemappings AT fangsu hybriditerativeschemebyarelaxedextragradientmethodforequilibriumproblemsageneralsystemofvariationalinequalitiesandfixedpointproblemsofacountablefamilyofnonexpansivemappings |