A Modified Halpern-TypeIterative Method of a System of Equilibrium Problems and a Fixed Point for a Totally Quasi-ϕ-Asymptotically Nonexpansive Mapping in a Banach Space
The purpose of this paper is to introduce the modified Halpern-type iterative method by the generalized f-projection operator for finding a common solution of fixed-point problem of a totally quasi-ϕ-asymptotically nonexpansive mapping and a system of equilibrium problems in a uniform smooth and str...
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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/10.1155/2012/750732 |
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| author | Preedaporn Kanjanasamranwong Poom Kumam Siwaporn Saewan |
| author_facet | Preedaporn Kanjanasamranwong Poom Kumam Siwaporn Saewan |
| author_sort | Preedaporn Kanjanasamranwong |
| collection | DOAJ |
| description | The purpose of this paper is to introduce the modified Halpern-type iterative method by the generalized f-projection operator for finding a common solution of fixed-point problem of a totally quasi-ϕ-asymptotically nonexpansive mapping and a system of equilibrium problems in a uniform smooth and
strictly convex Banach space with the Kadec-Klee property. Consequently, we prove the strong convergence for a common solution of above two sets. Our result presented in this paper generalize and improve
the result of Chang et al., (2012), and some others. |
| format | Article |
| id | doaj-art-94834608c8c04014bf676fcdd39ddff7 |
| 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-94834608c8c04014bf676fcdd39ddff72025-02-03T01:03:21ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/750732750732A Modified Halpern-TypeIterative Method of a System of Equilibrium Problems and a Fixed Point for a Totally Quasi-ϕ-Asymptotically Nonexpansive Mapping in a Banach SpacePreedaporn Kanjanasamranwong0Poom Kumam1Siwaporn Saewan2Department of Mathematics and Statistics, Faculty of Science, Thaksin University (TSU), Pa Phayom, Phatthalung 93110, ThailandDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangmod, Bangkok 10140, ThailandDepartment of Mathematics and Statistics, Faculty of Science, Thaksin University (TSU), Pa Phayom, Phatthalung 93110, ThailandThe purpose of this paper is to introduce the modified Halpern-type iterative method by the generalized f-projection operator for finding a common solution of fixed-point problem of a totally quasi-ϕ-asymptotically nonexpansive mapping and a system of equilibrium problems in a uniform smooth and strictly convex Banach space with the Kadec-Klee property. Consequently, we prove the strong convergence for a common solution of above two sets. Our result presented in this paper generalize and improve the result of Chang et al., (2012), and some others.http://dx.doi.org/10.1155/2012/750732 |
| spellingShingle | Preedaporn Kanjanasamranwong Poom Kumam Siwaporn Saewan A Modified Halpern-TypeIterative Method of a System of Equilibrium Problems and a Fixed Point for a Totally Quasi-ϕ-Asymptotically Nonexpansive Mapping in a Banach Space Journal of Applied Mathematics |
| title | A Modified Halpern-TypeIterative Method of a System of Equilibrium Problems and a Fixed Point for a Totally Quasi-ϕ-Asymptotically Nonexpansive Mapping in a Banach Space |
| title_full | A Modified Halpern-TypeIterative Method of a System of Equilibrium Problems and a Fixed Point for a Totally Quasi-ϕ-Asymptotically Nonexpansive Mapping in a Banach Space |
| title_fullStr | A Modified Halpern-TypeIterative Method of a System of Equilibrium Problems and a Fixed Point for a Totally Quasi-ϕ-Asymptotically Nonexpansive Mapping in a Banach Space |
| title_full_unstemmed | A Modified Halpern-TypeIterative Method of a System of Equilibrium Problems and a Fixed Point for a Totally Quasi-ϕ-Asymptotically Nonexpansive Mapping in a Banach Space |
| title_short | A Modified Halpern-TypeIterative Method of a System of Equilibrium Problems and a Fixed Point for a Totally Quasi-ϕ-Asymptotically Nonexpansive Mapping in a Banach Space |
| title_sort | modified halpern typeiterative method of a system of equilibrium problems and a fixed point for a totally quasi ϕ asymptotically nonexpansive mapping in a banach space |
| url | http://dx.doi.org/10.1155/2012/750732 |
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