Strong Convergence of a Hybrid Projection Algorithm for Equilibrium Problems, Variational Inequality Problems and Fixed Point Problems in a Banach Space
We introduce and study a new hybrid projection algorithm for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed points of relatively quasi-nonexpansive mappings, and the set of solutions of the variational inequality for an inverse-strongly-monotone o...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2009/613524 |
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| _version_ | 1832556598996762624 |
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| author | Wariam Chuayjan Sornsak Thianwan |
| author_facet | Wariam Chuayjan Sornsak Thianwan |
| author_sort | Wariam Chuayjan |
| collection | DOAJ |
| description | We introduce and study a new hybrid projection algorithm for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed points of relatively quasi-nonexpansive mappings, and the
set of solutions of the variational inequality for an inverse-strongly-monotone operator in a Banach space. Under suitable assumptions, we show a strong convergence theorem. Using this result, we obtain some applications in a Banach space. The results obtained in this paper extend and improve the several recent results in this area. |
| format | Article |
| id | doaj-art-2024cc2cac0a402e9285dd1ee4216f37 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-2024cc2cac0a402e9285dd1ee4216f372025-02-03T05:44:46ZengWileyAbstract and Applied Analysis1085-33751687-04092009-01-01200910.1155/2009/613524613524Strong Convergence of a Hybrid Projection Algorithm for Equilibrium Problems, Variational Inequality Problems and Fixed Point Problems in a Banach SpaceWariam Chuayjan0Sornsak Thianwan1Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, ThailandSchool of Science and Technology, Naresuan Phayao University, Phayao 56000, ThailandWe introduce and study a new hybrid projection algorithm for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed points of relatively quasi-nonexpansive mappings, and the set of solutions of the variational inequality for an inverse-strongly-monotone operator in a Banach space. Under suitable assumptions, we show a strong convergence theorem. Using this result, we obtain some applications in a Banach space. The results obtained in this paper extend and improve the several recent results in this area.http://dx.doi.org/10.1155/2009/613524 |
| spellingShingle | Wariam Chuayjan Sornsak Thianwan Strong Convergence of a Hybrid Projection Algorithm for Equilibrium Problems, Variational Inequality Problems and Fixed Point Problems in a Banach Space Abstract and Applied Analysis |
| title | Strong Convergence of a Hybrid Projection Algorithm for Equilibrium Problems, Variational Inequality Problems and Fixed Point Problems in a Banach Space |
| title_full | Strong Convergence of a Hybrid Projection Algorithm for Equilibrium Problems, Variational Inequality Problems and Fixed Point Problems in a Banach Space |
| title_fullStr | Strong Convergence of a Hybrid Projection Algorithm for Equilibrium Problems, Variational Inequality Problems and Fixed Point Problems in a Banach Space |
| title_full_unstemmed | Strong Convergence of a Hybrid Projection Algorithm for Equilibrium Problems, Variational Inequality Problems and Fixed Point Problems in a Banach Space |
| title_short | Strong Convergence of a Hybrid Projection Algorithm for Equilibrium Problems, Variational Inequality Problems and Fixed Point Problems in a Banach Space |
| title_sort | strong convergence of a hybrid projection algorithm for equilibrium problems variational inequality problems and fixed point problems in a banach space |
| url | http://dx.doi.org/10.1155/2009/613524 |
| work_keys_str_mv | AT wariamchuayjan strongconvergenceofahybridprojectionalgorithmforequilibriumproblemsvariationalinequalityproblemsandfixedpointproblemsinabanachspace AT sornsakthianwan strongconvergenceofahybridprojectionalgorithmforequilibriumproblemsvariationalinequalityproblemsandfixedpointproblemsinabanachspace |