Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces
We first introduce a new class of mappings called Bregman asymptotic pointwise nonexpansive mappings and investigate the existence and the approximation of fixed points of such mappings defined on a nonempty, bounded, closed, and convex subset C of a real Banach space E. Without using the original O...
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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/10.1155/2013/316813 |
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| _version_ | 1832567551521980416 |
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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 first introduce a new class of mappings called Bregman asymptotic pointwise nonexpansive mappings and investigate the existence and the approximation of fixed points of such mappings defined on a nonempty, bounded, closed, and convex subset C of a real Banach space E. Without using the original Opial property of a Banach space E, we prove weak convergence theorems for the sequences produced by generalized Mann and Ishikawa iteration processes for Bregman asymptotic pointwise nonexpansive mappings
in a reflexive Banach space E. Our results are applicable in the function spaces Lp, where 1<p<∞ is a real number. |
| format | Article |
| id | doaj-art-d7301ac359514dd19efa8419b5f1b318 |
| 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-d7301ac359514dd19efa8419b5f1b3182025-02-03T01:01:12ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/316813316813Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach SpacesChin-Tzong Pang0Eskandar Naraghirad1Department of Information Management, Yuan Ze University, Chung-Li 32003, TaiwanDepartment of Mathematics, Yasouj University, Yasouj 75918, IranWe first introduce a new class of mappings called Bregman asymptotic pointwise nonexpansive mappings and investigate the existence and the approximation of fixed points of such mappings defined on a nonempty, bounded, closed, and convex subset C of a real Banach space E. Without using the original Opial property of a Banach space E, we prove weak convergence theorems for the sequences produced by generalized Mann and Ishikawa iteration processes for Bregman asymptotic pointwise nonexpansive mappings in a reflexive Banach space E. Our results are applicable in the function spaces Lp, where 1<p<∞ is a real number.http://dx.doi.org/10.1155/2013/316813 |
| spellingShingle | Chin-Tzong Pang Eskandar Naraghirad Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces Abstract and Applied Analysis |
| title | Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces |
| title_full | Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces |
| title_fullStr | Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces |
| title_full_unstemmed | Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces |
| title_short | Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces |
| title_sort | bregman asymptotic pointwise nonexpansive mappings in banach spaces |
| url | http://dx.doi.org/10.1155/2013/316813 |
| work_keys_str_mv | AT chintzongpang bregmanasymptoticpointwisenonexpansivemappingsinbanachspaces AT eskandarnaraghirad bregmanasymptoticpointwisenonexpansivemappingsinbanachspaces |