Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems
The purpose of this paper is to introduce an iterative algorithm for finding a common element of the set of fixed points of quasi-nonexpansive mappings and the solution of split feasibility problems (SFP) and systems of equilibrium problems (SEP) in Hilbert spaces. We prove that the sequences genera...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/430409 |
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| _version_ | 1832556196409638912 |
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| author | Kamonrat Sombut Somyot Plubtieng |
| author_facet | Kamonrat Sombut Somyot Plubtieng |
| author_sort | Kamonrat Sombut |
| collection | DOAJ |
| description | The purpose of this paper is to introduce an iterative algorithm for finding a common element of the set of fixed points of quasi-nonexpansive mappings and the solution of split feasibility problems (SFP) and systems of equilibrium problems (SEP) in Hilbert spaces. We prove that the sequences generated by the proposed algorithm converge weakly to a common element of the fixed points set of quasi-nonexpansive mappings and the solution of split feasibility problems and systems of equilibrium problems under mild conditions. Our main result improves and extends the recent ones announced by Ceng et al. (2012) and many others. |
| format | Article |
| id | doaj-art-750ce9d768f2421181dfac800cebfb54 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-750ce9d768f2421181dfac800cebfb542025-02-03T05:46:07ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/430409430409Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium ProblemsKamonrat Sombut0Somyot Plubtieng1Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandDepartment of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandThe purpose of this paper is to introduce an iterative algorithm for finding a common element of the set of fixed points of quasi-nonexpansive mappings and the solution of split feasibility problems (SFP) and systems of equilibrium problems (SEP) in Hilbert spaces. We prove that the sequences generated by the proposed algorithm converge weakly to a common element of the fixed points set of quasi-nonexpansive mappings and the solution of split feasibility problems and systems of equilibrium problems under mild conditions. Our main result improves and extends the recent ones announced by Ceng et al. (2012) and many others.http://dx.doi.org/10.1155/2013/430409 |
| spellingShingle | Kamonrat Sombut Somyot Plubtieng Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems Abstract and Applied Analysis |
| title | Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems |
| title_full | Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems |
| title_fullStr | Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems |
| title_full_unstemmed | Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems |
| title_short | Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems |
| title_sort | weak convergence theorem for finding fixed points and solution of split feasibility and systems of equilibrium problems |
| url | http://dx.doi.org/10.1155/2013/430409 |
| work_keys_str_mv | AT kamonratsombut weakconvergencetheoremforfindingfixedpointsandsolutionofsplitfeasibilityandsystemsofequilibriumproblems AT somyotplubtieng weakconvergencetheoremforfindingfixedpointsandsolutionofsplitfeasibilityandsystemsofequilibriumproblems |