Convergence Theorems for Right Bregman Strongly Nonexpansive Mappings in Reflexive Banach Spaces
We prove a strong convergence theorem for a common fixed point of a finite family of right Bregman strongly nonexpansive mappings in the framework of real reflexive Banach spaces. Furthermore, we apply our method to approximate a common zero of a finite family of maximal monotone mappings and a sol...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/584395 |
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| _version_ | 1832562398214488064 |
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| author | H. Zegeye N. Shahzad |
| author_facet | H. Zegeye N. Shahzad |
| author_sort | H. Zegeye |
| collection | DOAJ |
| description | We prove a strong convergence theorem for a common fixed point of a finite family of right Bregman strongly nonexpansive mappings in the framework of real reflexive Banach spaces. Furthermore, we apply our method to approximate a common zero of a finite family of maximal monotone mappings and a solution of a finite family of convex feasibility problems in reflexive real Banach spaces. Our theorems complement some recent results that have been proved for this important class of nonlinear mappings. |
| format | Article |
| id | doaj-art-4d7d5079314e43df9ea8715f4710ac3b |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-4d7d5079314e43df9ea8715f4710ac3b2025-02-03T01:22:39ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/584395584395Convergence Theorems for Right Bregman Strongly Nonexpansive Mappings in Reflexive Banach SpacesH. Zegeye0N. Shahzad1Department of Mathematics, University of Botswana, Private, Bag 00704, Gaborone, BotswanaDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaWe prove a strong convergence theorem for a common fixed point of a finite family of right Bregman strongly nonexpansive mappings in the framework of real reflexive Banach spaces. Furthermore, we apply our method to approximate a common zero of a finite family of maximal monotone mappings and a solution of a finite family of convex feasibility problems in reflexive real Banach spaces. Our theorems complement some recent results that have been proved for this important class of nonlinear mappings.http://dx.doi.org/10.1155/2014/584395 |
| spellingShingle | H. Zegeye N. Shahzad Convergence Theorems for Right Bregman Strongly Nonexpansive Mappings in Reflexive Banach Spaces Abstract and Applied Analysis |
| title | Convergence Theorems for Right Bregman Strongly Nonexpansive Mappings in Reflexive Banach Spaces |
| title_full | Convergence Theorems for Right Bregman Strongly Nonexpansive Mappings in Reflexive Banach Spaces |
| title_fullStr | Convergence Theorems for Right Bregman Strongly Nonexpansive Mappings in Reflexive Banach Spaces |
| title_full_unstemmed | Convergence Theorems for Right Bregman Strongly Nonexpansive Mappings in Reflexive Banach Spaces |
| title_short | Convergence Theorems for Right Bregman Strongly Nonexpansive Mappings in Reflexive Banach Spaces |
| title_sort | convergence theorems for right bregman strongly nonexpansive mappings in reflexive banach spaces |
| url | http://dx.doi.org/10.1155/2014/584395 |
| work_keys_str_mv | AT hzegeye convergencetheoremsforrightbregmanstronglynonexpansivemappingsinreflexivebanachspaces AT nshahzad convergencetheoremsforrightbregmanstronglynonexpansivemappingsinreflexivebanachspaces |