Strong Convergence Theorems for Quasi-Bregman Nonexpansive Mappings in Reflexive Banach Spaces
We study a strong convergence for a common fixed point of a finite family of quasi-Bregman nonexpansive mappings in the framework of real reflexive Banach spaces. As a consequence, convergence for a common fixed point of a finite family of Bergman relatively nonexpansive mappings is discussed. Furth...
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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/10.1155/2014/580686 |
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| _version_ | 1832548156819111936 |
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| author | Mohammed Ali Alghamdi Naseer Shahzad Habtu Zegeye |
| author_facet | Mohammed Ali Alghamdi Naseer Shahzad Habtu Zegeye |
| author_sort | Mohammed Ali Alghamdi |
| collection | DOAJ |
| description | We study a strong convergence for a common fixed point of a
finite family of quasi-Bregman nonexpansive mappings in the framework of
real reflexive Banach spaces. As a consequence, convergence for a common
fixed point of a finite family of Bergman relatively nonexpansive mappings is
discussed. Furthermore, we apply our method to prove strong convergence theorems
of iterative algorithms for finding a common solution of a finite family
equilibrium problem and a common zero of a finite family of maximal monotone
mappings. Our theorems improve and unify most of the results that have
been proved for this important class of nonlinear mappings. |
| format | Article |
| id | doaj-art-e44721ee63e24b2597f012720d38bae7 |
| 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-e44721ee63e24b2597f012720d38bae72025-02-03T06:42:03ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/580686580686Strong Convergence Theorems for Quasi-Bregman Nonexpansive Mappings in Reflexive Banach SpacesMohammed Ali Alghamdi0Naseer Shahzad1Habtu Zegeye2Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, University of Botswana, Private Bag 00704, Gaborone, BotswanaWe study a strong convergence for a common fixed point of a finite family of quasi-Bregman nonexpansive mappings in the framework of real reflexive Banach spaces. As a consequence, convergence for a common fixed point of a finite family of Bergman relatively nonexpansive mappings is discussed. Furthermore, we apply our method to prove strong convergence theorems of iterative algorithms for finding a common solution of a finite family equilibrium problem and a common zero of a finite family of maximal monotone mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.http://dx.doi.org/10.1155/2014/580686 |
| spellingShingle | Mohammed Ali Alghamdi Naseer Shahzad Habtu Zegeye Strong Convergence Theorems for Quasi-Bregman Nonexpansive Mappings in Reflexive Banach Spaces Journal of Applied Mathematics |
| title | Strong Convergence Theorems for Quasi-Bregman Nonexpansive Mappings in Reflexive Banach Spaces |
| title_full | Strong Convergence Theorems for Quasi-Bregman Nonexpansive Mappings in Reflexive Banach Spaces |
| title_fullStr | Strong Convergence Theorems for Quasi-Bregman Nonexpansive Mappings in Reflexive Banach Spaces |
| title_full_unstemmed | Strong Convergence Theorems for Quasi-Bregman Nonexpansive Mappings in Reflexive Banach Spaces |
| title_short | Strong Convergence Theorems for Quasi-Bregman Nonexpansive Mappings in Reflexive Banach Spaces |
| title_sort | strong convergence theorems for quasi bregman nonexpansive mappings in reflexive banach spaces |
| url | http://dx.doi.org/10.1155/2014/580686 |
| work_keys_str_mv | AT mohammedalialghamdi strongconvergencetheoremsforquasibregmannonexpansivemappingsinreflexivebanachspaces AT naseershahzad strongconvergencetheoremsforquasibregmannonexpansivemappingsinreflexivebanachspaces AT habtuzegeye strongconvergencetheoremsforquasibregmannonexpansivemappingsinreflexivebanachspaces |