Implicit Iterative Scheme for a Countable Family of Nonexpansive Mappings in 2-Uniformly Smooth Banach Spaces
Implicit Mann process and Halpern-type iteration have been extensively studied by many others. In this paper, in order to find a common fixed point of a countable family of nonexpansive mappings in the framework of Banach spaces, we propose a new implicit iterative algorithm related to a strongly ac...
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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/10.1155/2013/264910 |
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| author | Ming Tian Xin Jin |
| author_facet | Ming Tian Xin Jin |
| author_sort | Ming Tian |
| collection | DOAJ |
| description | Implicit Mann process and Halpern-type iteration have been extensively studied by many others. In this paper, in order to find a common fixed point of a countable family of nonexpansive mappings in the framework of Banach spaces, we propose a new implicit iterative algorithm related to a strongly accretive and Lipschitzian continuous operator F:xn=αnγV(xn)+βnxn-1+((1-βn)I-αnμF)Tnxn and get strong convergence under some mild assumptions. Our results improve and extend the corresponding conclusions announced by many others. |
| format | Article |
| id | doaj-art-8bab47da1cc3474da3dc6157f7e97f00 |
| 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-8bab47da1cc3474da3dc6157f7e97f002025-08-20T03:37:41ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/264910264910Implicit Iterative Scheme for a Countable Family of Nonexpansive Mappings in 2-Uniformly Smooth Banach SpacesMing Tian0Xin Jin1College of Science, Civil Aviation University of China, Tianjin 300300, ChinaCollege of Science, Civil Aviation University of China, Tianjin 300300, ChinaImplicit Mann process and Halpern-type iteration have been extensively studied by many others. In this paper, in order to find a common fixed point of a countable family of nonexpansive mappings in the framework of Banach spaces, we propose a new implicit iterative algorithm related to a strongly accretive and Lipschitzian continuous operator F:xn=αnγV(xn)+βnxn-1+((1-βn)I-αnμF)Tnxn and get strong convergence under some mild assumptions. Our results improve and extend the corresponding conclusions announced by many others.http://dx.doi.org/10.1155/2013/264910 |
| spellingShingle | Ming Tian Xin Jin Implicit Iterative Scheme for a Countable Family of Nonexpansive Mappings in 2-Uniformly Smooth Banach Spaces Abstract and Applied Analysis |
| title | Implicit Iterative Scheme for a Countable Family of Nonexpansive Mappings in 2-Uniformly Smooth Banach Spaces |
| title_full | Implicit Iterative Scheme for a Countable Family of Nonexpansive Mappings in 2-Uniformly Smooth Banach Spaces |
| title_fullStr | Implicit Iterative Scheme for a Countable Family of Nonexpansive Mappings in 2-Uniformly Smooth Banach Spaces |
| title_full_unstemmed | Implicit Iterative Scheme for a Countable Family of Nonexpansive Mappings in 2-Uniformly Smooth Banach Spaces |
| title_short | Implicit Iterative Scheme for a Countable Family of Nonexpansive Mappings in 2-Uniformly Smooth Banach Spaces |
| title_sort | implicit iterative scheme for a countable family of nonexpansive mappings in 2 uniformly smooth banach spaces |
| url | http://dx.doi.org/10.1155/2013/264910 |
| work_keys_str_mv | AT mingtian implicititerativeschemeforacountablefamilyofnonexpansivemappingsin2uniformlysmoothbanachspaces AT xinjin implicititerativeschemeforacountablefamilyofnonexpansivemappingsin2uniformlysmoothbanachspaces |