Convergence Theorems for Infinite Family of Multivalued Quasi-Nonexpansive Mappings in Uniformly Convex Banach Spaces
We introduce an iterative method for finding a common fixed point of a countable family of multivalued quasi-nonexpansive mapping {Ti} in a uniformly convex Banach space. We prove that under certain control conditions, the iterative sequence generated by our method is an approximating fixed point se...
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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/10.1155/2012/435790 |
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| author | Aunyarat Bunyawat Suthep Suantai |
| author_facet | Aunyarat Bunyawat Suthep Suantai |
| author_sort | Aunyarat Bunyawat |
| collection | DOAJ |
| description | We introduce an iterative method for finding a common fixed point of a countable family of multivalued quasi-nonexpansive mapping {Ti} in a uniformly convex Banach space. We prove that under certain control conditions, the iterative sequence generated by our method is an approximating fixed point sequence of each Ti. Some strong convergence theorems of the proposed method are also obtained for the following cases: all Ti are continuous and one of Ti is hemicompact, and the domain K is compact. |
| format | Article |
| id | doaj-art-2c969ad3609543cda5b09e22886a5521 |
| 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-2c969ad3609543cda5b09e22886a55212025-02-03T01:01:03ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/435790435790Convergence Theorems for Infinite Family of Multivalued Quasi-Nonexpansive Mappings in Uniformly Convex Banach SpacesAunyarat Bunyawat0Suthep Suantai1Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandDepartment of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandWe introduce an iterative method for finding a common fixed point of a countable family of multivalued quasi-nonexpansive mapping {Ti} in a uniformly convex Banach space. We prove that under certain control conditions, the iterative sequence generated by our method is an approximating fixed point sequence of each Ti. Some strong convergence theorems of the proposed method are also obtained for the following cases: all Ti are continuous and one of Ti is hemicompact, and the domain K is compact.http://dx.doi.org/10.1155/2012/435790 |
| spellingShingle | Aunyarat Bunyawat Suthep Suantai Convergence Theorems for Infinite Family of Multivalued Quasi-Nonexpansive Mappings in Uniformly Convex Banach Spaces Abstract and Applied Analysis |
| title | Convergence Theorems for Infinite Family of Multivalued Quasi-Nonexpansive Mappings in Uniformly Convex Banach Spaces |
| title_full | Convergence Theorems for Infinite Family of Multivalued Quasi-Nonexpansive Mappings in Uniformly Convex Banach Spaces |
| title_fullStr | Convergence Theorems for Infinite Family of Multivalued Quasi-Nonexpansive Mappings in Uniformly Convex Banach Spaces |
| title_full_unstemmed | Convergence Theorems for Infinite Family of Multivalued Quasi-Nonexpansive Mappings in Uniformly Convex Banach Spaces |
| title_short | Convergence Theorems for Infinite Family of Multivalued Quasi-Nonexpansive Mappings in Uniformly Convex Banach Spaces |
| title_sort | convergence theorems for infinite family of multivalued quasi nonexpansive mappings in uniformly convex banach spaces |
| url | http://dx.doi.org/10.1155/2012/435790 |
| work_keys_str_mv | AT aunyaratbunyawat convergencetheoremsforinfinitefamilyofmultivaluedquasinonexpansivemappingsinuniformlyconvexbanachspaces AT suthepsuantai convergencetheoremsforinfinitefamilyofmultivaluedquasinonexpansivemappingsinuniformlyconvexbanachspaces |