A New Hybrid Algorithm for a Pair of Quasi-𝜙-Asymptotically Nonexpansive Mappings and Generalized Mixed Equilibrium Problems in Banach Spaces
The purpose of this paper is, by using a new hybrid method, to prove a strong convergence theorem for finding a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for a variational inequality problem, and the set of common fixed points for a pair...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/956852 |
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| _version_ | 1832549111198384128 |
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| author | Jinhua Zhu Shih-Sen Chang |
| author_facet | Jinhua Zhu Shih-Sen Chang |
| author_sort | Jinhua Zhu |
| collection | DOAJ |
| description | The purpose of this paper is, by using a new hybrid method, to prove a strong
convergence theorem for finding a common element of the set of solutions for a generalized
mixed equilibrium problem, the set of solutions for a variational inequality problem, and
the set of common fixed points for a pair of quasi-𝜙-asymptotically nonexpansive mappings.
Under suitable conditions some strong convergence theorems are established in a 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-8384e6250afe4a909d4573d0c589e2d3 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8384e6250afe4a909d4573d0c589e2d32025-02-03T06:12:07ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/956852956852A New Hybrid Algorithm for a Pair of Quasi-𝜙-Asymptotically Nonexpansive Mappings and Generalized Mixed Equilibrium Problems in Banach SpacesJinhua Zhu0Shih-Sen Chang1Department of Mathematics, Yibin University, Yibin 644007, ChinaDepartment of Mathematics, Yibin University, Yibin 644007, ChinaThe purpose of this paper is, by using a new hybrid method, to prove a strong convergence theorem for finding a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for a variational inequality problem, and the set of common fixed points for a pair of quasi-𝜙-asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in a 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/10.1155/2011/956852 |
| spellingShingle | Jinhua Zhu Shih-Sen Chang A New Hybrid Algorithm for a Pair of Quasi-𝜙-Asymptotically Nonexpansive Mappings and Generalized Mixed Equilibrium Problems in Banach Spaces International Journal of Mathematics and Mathematical Sciences |
| title | A New Hybrid Algorithm for a Pair of Quasi-𝜙-Asymptotically Nonexpansive Mappings and Generalized Mixed Equilibrium Problems in Banach Spaces |
| title_full | A New Hybrid Algorithm for a Pair of Quasi-𝜙-Asymptotically Nonexpansive Mappings and Generalized Mixed Equilibrium Problems in Banach Spaces |
| title_fullStr | A New Hybrid Algorithm for a Pair of Quasi-𝜙-Asymptotically Nonexpansive Mappings and Generalized Mixed Equilibrium Problems in Banach Spaces |
| title_full_unstemmed | A New Hybrid Algorithm for a Pair of Quasi-𝜙-Asymptotically Nonexpansive Mappings and Generalized Mixed Equilibrium Problems in Banach Spaces |
| title_short | A New Hybrid Algorithm for a Pair of Quasi-𝜙-Asymptotically Nonexpansive Mappings and Generalized Mixed Equilibrium Problems in Banach Spaces |
| title_sort | new hybrid algorithm for a pair of quasi 𝜙 asymptotically nonexpansive mappings and generalized mixed equilibrium problems in banach spaces |
| url | http://dx.doi.org/10.1155/2011/956852 |
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