Strong Convergence Theorems for Countable Families of Uniformly Quasi-ϕ-Asymptotically Nonexpansive Mappings and a System of Generalized Mixed Equilibrium Problems
The purpose of this paper is to present a new hybrid block iterative scheme by the generalized f- projection method for finding a common element of the fixed point set for a countable family of uniformly quasi-ϕ-asymptotically nonexpansive mappings and the set of solutions of the system of generaliz...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/701675 |
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| _version_ | 1832551875079045120 |
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| author | Siwaporn Saewan Poom Kumam |
| author_facet | Siwaporn Saewan Poom Kumam |
| author_sort | Siwaporn Saewan |
| collection | DOAJ |
| description | The purpose of this paper is to present a new hybrid block iterative scheme by the generalized f-
projection method for finding a common element of the fixed point set for a countable family of uniformly
quasi-ϕ-asymptotically nonexpansive mappings and the set of solutions of the system of generalized mixed
equilibrium problems in a strictly convex and uniformly smooth Banach space with the Kadec-Klee
property. Furthermore, we prove that our new iterative scheme converges strongly to a common element
of the aforementioned sets. The results presented in this paper improve and extend important recent
results in the literature. |
| format | Article |
| id | doaj-art-5d028128ebb44c2983e333727f1c15fb |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5d028128ebb44c2983e333727f1c15fb2025-02-03T06:00:15ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/701675701675Strong Convergence Theorems for Countable Families of Uniformly Quasi-ϕ-Asymptotically Nonexpansive Mappings and a System of Generalized Mixed Equilibrium ProblemsSiwaporn Saewan0Poom 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, ThailandThe purpose of this paper is to present a new hybrid block iterative scheme by the generalized f- projection method for finding a common element of the fixed point set for a countable family of uniformly quasi-ϕ-asymptotically nonexpansive mappings and the set of solutions of the system of generalized mixed equilibrium problems in a strictly convex and uniformly smooth Banach space with the Kadec-Klee property. Furthermore, we prove that our new iterative scheme converges strongly to a common element of the aforementioned sets. The results presented in this paper improve and extend important recent results in the literature.http://dx.doi.org/10.1155/2011/701675 |
| spellingShingle | Siwaporn Saewan Poom Kumam Strong Convergence Theorems for Countable Families of Uniformly Quasi-ϕ-Asymptotically Nonexpansive Mappings and a System of Generalized Mixed Equilibrium Problems Abstract and Applied Analysis |
| title | Strong Convergence Theorems for Countable Families of Uniformly Quasi-ϕ-Asymptotically Nonexpansive Mappings and a System of Generalized Mixed Equilibrium Problems |
| title_full | Strong Convergence Theorems for Countable Families of Uniformly Quasi-ϕ-Asymptotically Nonexpansive Mappings and a System of Generalized Mixed Equilibrium Problems |
| title_fullStr | Strong Convergence Theorems for Countable Families of Uniformly Quasi-ϕ-Asymptotically Nonexpansive Mappings and a System of Generalized Mixed Equilibrium Problems |
| title_full_unstemmed | Strong Convergence Theorems for Countable Families of Uniformly Quasi-ϕ-Asymptotically Nonexpansive Mappings and a System of Generalized Mixed Equilibrium Problems |
| title_short | Strong Convergence Theorems for Countable Families of Uniformly Quasi-ϕ-Asymptotically Nonexpansive Mappings and a System of Generalized Mixed Equilibrium Problems |
| title_sort | strong convergence theorems for countable families of uniformly quasi ϕ asymptotically nonexpansive mappings and a system of generalized mixed equilibrium problems |
| url | http://dx.doi.org/10.1155/2011/701675 |
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