Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces
The purpose of this paper is first to introduce the concept of total quasi-ϕ-asymptotically nonexpansive mapping which contains many kinds of mappings as its special cases and then to use a hybrid algorithm to introduce a new iterative scheme for finding a common element of the set of solutions for...
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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/10.1155/2012/961560 |
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| _version_ | 1832565479767539712 |
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| author | Jinhua Zhu Shih-Sen Chang Min Liu |
| author_facet | Jinhua Zhu Shih-Sen Chang Min Liu |
| author_sort | Jinhua Zhu |
| collection | DOAJ |
| description | The purpose of this paper is first to introduce the concept of total quasi-ϕ-asymptotically nonexpansive mapping which contains many kinds of mappings as its special cases and then to use a hybrid algorithm to introduce a new iterative scheme for
finding a common element of the set of solutions for a system of generalized mixed equilibrium problems and the set of common fixed points for a countable family of total quasi-ϕ-asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in an uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in the paper improve and extend some recent results. |
| format | Article |
| id | doaj-art-eae2d66c4742491ca10f9d825776a06e |
| 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-eae2d66c4742491ca10f9d825776a06e2025-02-03T01:07:43ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/961560961560Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach SpacesJinhua Zhu0Shih-Sen Chang1Min Liu2Department of Mathematics, Yibin University, Yibin, Sichuan 644007, ChinaDepartment of Mathematics, College of Statistics and Mathematics, Yunnan University of Finance and Economics, Yunnan, Kunming 650221, ChinaDepartment of Mathematics, Yibin University, Yibin, Sichuan 644007, ChinaThe purpose of this paper is first to introduce the concept of total quasi-ϕ-asymptotically nonexpansive mapping which contains many kinds of mappings as its special cases and then to use a hybrid algorithm to introduce a new iterative scheme for finding a common element of the set of solutions for a system of generalized mixed equilibrium problems and the set of common fixed points for a countable family of total quasi-ϕ-asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in an uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in the paper improve and extend some recent results.http://dx.doi.org/10.1155/2012/961560 |
| spellingShingle | Jinhua Zhu Shih-Sen Chang Min Liu Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces Journal of Applied Mathematics |
| title | Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces |
| title_full | Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces |
| title_fullStr | Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces |
| title_full_unstemmed | Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces |
| title_short | Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces |
| title_sort | generalized mixed equilibrium problems and fixed point problem for a countable family of total quasi ϕ asymptotically nonexpansive mappings in banach spaces |
| url | http://dx.doi.org/10.1155/2012/961560 |
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