Weak Convergence Theorems for Bregman Relatively Nonexpansive Mappings in Banach Spaces
We study Mann type iterative algorithms for finding fixed points of Bregman relatively nonexpansive mappings in Banach spaces. By exhibiting an example, we first show that the class of Bregman relatively nonexpansive mappings embraces properly the class of Bregman strongly nonexpansive mappings whic...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/573075 |
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| _version_ | 1832548088543182848 |
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| author | Chin-Tzong Pang Eskandar Naraghirad Ching-Feng Wen |
| author_facet | Chin-Tzong Pang Eskandar Naraghirad Ching-Feng Wen |
| author_sort | Chin-Tzong Pang |
| collection | DOAJ |
| description | We study Mann type iterative algorithms for finding fixed points of Bregman relatively nonexpansive mappings in Banach spaces. By exhibiting an example, we first show that the class of Bregman relatively nonexpansive mappings embraces properly the class of Bregman strongly nonexpansive mappings which was investigated by Martín-Márques et al. (2013). We then prove weak convergence theorems for the sequences produced by the methods. Some application of our results to the problem of finding a zero of a maximal monotone operator in a Banach space is presented. Our results improve and generalize many known results in the current literature. |
| format | Article |
| id | doaj-art-d3d45f65e72a452d885e2fb3d139fdfd |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-d3d45f65e72a452d885e2fb3d139fdfd2025-02-03T06:42:16ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/573075573075Weak Convergence Theorems for Bregman Relatively Nonexpansive Mappings in Banach SpacesChin-Tzong Pang0Eskandar Naraghirad1Ching-Feng Wen2Department of Information Management, and Innovation Center for Big Data and Digital Convergence, Yuan Ze University, Chung-Li 32003, TaiwanDepartment of Mathematics, Yasouj University, Yasouj 75918, IranCenter for Fundamental Science, Kaohsiung Medical University, Kaohsiung 807, TaiwanWe study Mann type iterative algorithms for finding fixed points of Bregman relatively nonexpansive mappings in Banach spaces. By exhibiting an example, we first show that the class of Bregman relatively nonexpansive mappings embraces properly the class of Bregman strongly nonexpansive mappings which was investigated by Martín-Márques et al. (2013). We then prove weak convergence theorems for the sequences produced by the methods. Some application of our results to the problem of finding a zero of a maximal monotone operator in a Banach space is presented. Our results improve and generalize many known results in the current literature.http://dx.doi.org/10.1155/2014/573075 |
| spellingShingle | Chin-Tzong Pang Eskandar Naraghirad Ching-Feng Wen Weak Convergence Theorems for Bregman Relatively Nonexpansive Mappings in Banach Spaces Journal of Applied Mathematics |
| title | Weak Convergence Theorems for Bregman Relatively Nonexpansive Mappings in Banach Spaces |
| title_full | Weak Convergence Theorems for Bregman Relatively Nonexpansive Mappings in Banach Spaces |
| title_fullStr | Weak Convergence Theorems for Bregman Relatively Nonexpansive Mappings in Banach Spaces |
| title_full_unstemmed | Weak Convergence Theorems for Bregman Relatively Nonexpansive Mappings in Banach Spaces |
| title_short | Weak Convergence Theorems for Bregman Relatively Nonexpansive Mappings in Banach Spaces |
| title_sort | weak convergence theorems for bregman relatively nonexpansive mappings in banach spaces |
| url | http://dx.doi.org/10.1155/2014/573075 |
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