Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space
We introduce a hybrid iterative scheme for finding a common element of the set of common fixed points for a family of infinitely nonexpansive mappings, the set of solutions of the varitional inequality problem and the equilibrium problem in Hilbert space. Under suitable conditions, some strong conve...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/232541 |
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| author | Zhou Yinying Cao Jiantao Wang Yali |
| author_facet | Zhou Yinying Cao Jiantao Wang Yali |
| author_sort | Zhou Yinying |
| collection | DOAJ |
| description | We introduce a hybrid iterative scheme for finding a common element of the set of common fixed points for a family of infinitely nonexpansive mappings, the set of solutions of the varitional inequality problem and the equilibrium problem in Hilbert space. Under suitable conditions, some strong convergence theorems are obtained. Our results improve and extend the corresponding results in (Chang et al. (2009), Min and Chang (2012), Plubtieng and Punpaeng (2007), S. Takahashi and W. Takahashi (2007), Tada and Takahashi (2007), Gang and Changsong (2009), Ying (2013), Y. Yao and J. C. Yao (2007), and Yong-Cho and Kang (2012)). |
| format | Article |
| id | doaj-art-ba4be05b43d44303a6d9a0ff1a1dc0e8 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-ba4be05b43d44303a6d9a0ff1a1dc0e82025-02-03T05:52:21ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/232541232541Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert SpaceZhou Yinying0Cao Jiantao1Wang Yali2Department of Mathematics and Information Sciences, Langfang Teachers College, Langfang, Hebei 065000, ChinaDepartment of Mathematics and Information Sciences, Langfang Teachers College, Langfang, Hebei 065000, ChinaDepartment of Mathematics and Information Sciences, Langfang Teachers College, Langfang, Hebei 065000, ChinaWe introduce a hybrid iterative scheme for finding a common element of the set of common fixed points for a family of infinitely nonexpansive mappings, the set of solutions of the varitional inequality problem and the equilibrium problem in Hilbert space. Under suitable conditions, some strong convergence theorems are obtained. Our results improve and extend the corresponding results in (Chang et al. (2009), Min and Chang (2012), Plubtieng and Punpaeng (2007), S. Takahashi and W. Takahashi (2007), Tada and Takahashi (2007), Gang and Changsong (2009), Ying (2013), Y. Yao and J. C. Yao (2007), and Yong-Cho and Kang (2012)).http://dx.doi.org/10.1155/2014/232541 |
| spellingShingle | Zhou Yinying Cao Jiantao Wang Yali Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space Journal of Applied Mathematics |
| title | Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space |
| title_full | Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space |
| title_fullStr | Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space |
| title_full_unstemmed | Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space |
| title_short | Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space |
| title_sort | convergence theorem for equilibrium and variational inequality problems and a family of infinitely nonexpansive mappings in hilbert space |
| url | http://dx.doi.org/10.1155/2014/232541 |
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