An Iterative Shrinking Projection Method for Solving Fixed Point Problems of Closed and ϕ-Quasi-Strict Pseudocontractions along with Generalized Mixed Equilibrium Problems in Banach Spaces
We provide some new type of mappings associated with pseudocontractions by introducing some actual examples in smooth and strictly convex Banach spaces. Moreover, we also find the significant inequality related to the mappings mentioned in the paper and the mappings defined from generalized mixed eq...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/536283 |
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| author | Kasamsuk Ungchittrakool |
| author_facet | Kasamsuk Ungchittrakool |
| author_sort | Kasamsuk Ungchittrakool |
| collection | DOAJ |
| description | We provide some new type of mappings associated with pseudocontractions by introducing some actual examples in smooth and strictly convex Banach spaces. Moreover, we also find the significant inequality related to the mappings mentioned in the paper and the mappings defined from generalized mixed equilibrium problems on Banach spaces. We propose an iterative shrinking projection method for finding a common solution of generalized mixed equilibrium problems and fixed point problems of closed and ϕ-quasi-strict pseudo-contractions. Our results hold in reflexive, strictly convex, and smooth Banach spaces with the property (K). The results of this paper improve and extend the corresponding results of Zhou and Gao (2010) and many others. |
| format | Article |
| id | doaj-art-43b7e7f92d944400aeede5608e3994cf |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-43b7e7f92d944400aeede5608e3994cf2025-02-03T01:00:58ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/536283536283An Iterative Shrinking Projection Method for Solving Fixed Point Problems of Closed and ϕ-Quasi-Strict Pseudocontractions along with Generalized Mixed Equilibrium Problems in Banach SpacesKasamsuk Ungchittrakool0Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandWe provide some new type of mappings associated with pseudocontractions by introducing some actual examples in smooth and strictly convex Banach spaces. Moreover, we also find the significant inequality related to the mappings mentioned in the paper and the mappings defined from generalized mixed equilibrium problems on Banach spaces. We propose an iterative shrinking projection method for finding a common solution of generalized mixed equilibrium problems and fixed point problems of closed and ϕ-quasi-strict pseudo-contractions. Our results hold in reflexive, strictly convex, and smooth Banach spaces with the property (K). The results of this paper improve and extend the corresponding results of Zhou and Gao (2010) and many others.http://dx.doi.org/10.1155/2012/536283 |
| spellingShingle | Kasamsuk Ungchittrakool An Iterative Shrinking Projection Method for Solving Fixed Point Problems of Closed and ϕ-Quasi-Strict Pseudocontractions along with Generalized Mixed Equilibrium Problems in Banach Spaces Abstract and Applied Analysis |
| title | An Iterative Shrinking Projection Method for Solving Fixed Point Problems of Closed and ϕ-Quasi-Strict Pseudocontractions along with Generalized Mixed Equilibrium Problems in Banach Spaces |
| title_full | An Iterative Shrinking Projection Method for Solving Fixed Point Problems of Closed and ϕ-Quasi-Strict Pseudocontractions along with Generalized Mixed Equilibrium Problems in Banach Spaces |
| title_fullStr | An Iterative Shrinking Projection Method for Solving Fixed Point Problems of Closed and ϕ-Quasi-Strict Pseudocontractions along with Generalized Mixed Equilibrium Problems in Banach Spaces |
| title_full_unstemmed | An Iterative Shrinking Projection Method for Solving Fixed Point Problems of Closed and ϕ-Quasi-Strict Pseudocontractions along with Generalized Mixed Equilibrium Problems in Banach Spaces |
| title_short | An Iterative Shrinking Projection Method for Solving Fixed Point Problems of Closed and ϕ-Quasi-Strict Pseudocontractions along with Generalized Mixed Equilibrium Problems in Banach Spaces |
| title_sort | iterative shrinking projection method for solving fixed point problems of closed and ϕ quasi strict pseudocontractions along with generalized mixed equilibrium problems in banach spaces |
| url | http://dx.doi.org/10.1155/2012/536283 |
| work_keys_str_mv | AT kasamsukungchittrakool aniterativeshrinkingprojectionmethodforsolvingfixedpointproblemsofclosedandphquasistrictpseudocontractionsalongwithgeneralizedmixedequilibriumproblemsinbanachspaces AT kasamsukungchittrakool iterativeshrinkingprojectionmethodforsolvingfixedpointproblemsofclosedandphquasistrictpseudocontractionsalongwithgeneralizedmixedequilibriumproblemsinbanachspaces |