Strong Convergence of a General Iterative Method for a Countable Family of Nonexpansive Mappings in Banach Spaces
We introduce a general algorithm to approximate common fixed points for a countable family of nonexpansive mappings in a real Banach space. We prove strong convergence theorems for the sequences produced by the methods and approximate a common fixed point of a countable family of nonexpansive mappin...
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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/10.1155/2013/539061 |
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| _version_ | 1832565354590633984 |
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| author | Chin-Tzong Pang Eskandar Naraghirad |
| author_facet | Chin-Tzong Pang Eskandar Naraghirad |
| author_sort | Chin-Tzong Pang |
| collection | DOAJ |
| description | We introduce a general algorithm to approximate common fixed points for a countable family of nonexpansive mappings in a real Banach space. We prove strong convergence theorems for the sequences produced by the methods and approximate a common fixed point of a countable family of nonexpansive mappings which solves uniquely the corresponding variational inequality. Furthermore, we apply our results for finding a zero of an accretive operator. It is important to state clearly that the contribution of this paper in relation with the previous works (Marino and Xu, 2006) is a technical method to prove strong convergence theorems of a general iterative algorithm for an infinite family of nonexpansive mappings in Banach spaces. Our results improve and generalize many known results in the current literature. |
| format | Article |
| id | doaj-art-1bf9cde293c949368ffee7915382ad1f |
| 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-1bf9cde293c949368ffee7915382ad1f2025-02-03T01:08:00ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/539061539061Strong Convergence of a General Iterative Method for a Countable Family of Nonexpansive Mappings in Banach SpacesChin-Tzong Pang0Eskandar Naraghirad1Department of Information Management, Yuan Ze University, Chungli 32003, TaiwanDepartment of Mathematics, Yasouj University, Yasouj 75918, IranWe introduce a general algorithm to approximate common fixed points for a countable family of nonexpansive mappings in a real Banach space. We prove strong convergence theorems for the sequences produced by the methods and approximate a common fixed point of a countable family of nonexpansive mappings which solves uniquely the corresponding variational inequality. Furthermore, we apply our results for finding a zero of an accretive operator. It is important to state clearly that the contribution of this paper in relation with the previous works (Marino and Xu, 2006) is a technical method to prove strong convergence theorems of a general iterative algorithm for an infinite family of nonexpansive mappings in Banach spaces. Our results improve and generalize many known results in the current literature.http://dx.doi.org/10.1155/2013/539061 |
| spellingShingle | Chin-Tzong Pang Eskandar Naraghirad Strong Convergence of a General Iterative Method for a Countable Family of Nonexpansive Mappings in Banach Spaces Abstract and Applied Analysis |
| title | Strong Convergence of a General Iterative Method for a Countable Family of Nonexpansive Mappings in Banach Spaces |
| title_full | Strong Convergence of a General Iterative Method for a Countable Family of Nonexpansive Mappings in Banach Spaces |
| title_fullStr | Strong Convergence of a General Iterative Method for a Countable Family of Nonexpansive Mappings in Banach Spaces |
| title_full_unstemmed | Strong Convergence of a General Iterative Method for a Countable Family of Nonexpansive Mappings in Banach Spaces |
| title_short | Strong Convergence of a General Iterative Method for a Countable Family of Nonexpansive Mappings in Banach Spaces |
| title_sort | strong convergence of a general iterative method for a countable family of nonexpansive mappings in banach spaces |
| url | http://dx.doi.org/10.1155/2013/539061 |
| work_keys_str_mv | AT chintzongpang strongconvergenceofageneraliterativemethodforacountablefamilyofnonexpansivemappingsinbanachspaces AT eskandarnaraghirad strongconvergenceofageneraliterativemethodforacountablefamilyofnonexpansivemappingsinbanachspaces |