Strong Convergence Iterative Algorithms for Equilibrium Problems and Fixed Point Problems in Banach Spaces
We first introduce the concept of Bregman asymptotically quasinonexpansive mappings and prove that the fixed point set of this kind of mappings is closed and convex. Then we construct an iterative scheme to find a common element of the set of solutions of an equilibrium problem and the set of common...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/619762 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832560459169923072 |
|---|---|
| author | Shenghua Wang Shin Min Kang |
| author_facet | Shenghua Wang Shin Min Kang |
| author_sort | Shenghua Wang |
| collection | DOAJ |
| description | We first introduce the concept of Bregman asymptotically quasinonexpansive mappings and prove that the fixed point set of this kind of mappings is closed and convex. Then we construct an iterative scheme to find a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a countable family of Bregman asymptotically quasinonexpansive mappings in reflexive Banach spaces and prove strong convergence theorems. Our results extend the recent ones of some others. |
| format | Article |
| id | doaj-art-0119bca8c515447cbd6bfba96fabf97e |
| 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-0119bca8c515447cbd6bfba96fabf97e2025-02-03T01:27:31ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/619762619762Strong Convergence Iterative Algorithms for Equilibrium Problems and Fixed Point Problems in Banach SpacesShenghua Wang0Shin Min Kang1Department of Applied Mathematics and Physics, North China Electric Power University, Baoding 071003, ChinaDepartment of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of KoreaWe first introduce the concept of Bregman asymptotically quasinonexpansive mappings and prove that the fixed point set of this kind of mappings is closed and convex. Then we construct an iterative scheme to find a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a countable family of Bregman asymptotically quasinonexpansive mappings in reflexive Banach spaces and prove strong convergence theorems. Our results extend the recent ones of some others.http://dx.doi.org/10.1155/2013/619762 |
| spellingShingle | Shenghua Wang Shin Min Kang Strong Convergence Iterative Algorithms for Equilibrium Problems and Fixed Point Problems in Banach Spaces Abstract and Applied Analysis |
| title | Strong Convergence Iterative Algorithms for Equilibrium Problems and Fixed Point Problems in Banach Spaces |
| title_full | Strong Convergence Iterative Algorithms for Equilibrium Problems and Fixed Point Problems in Banach Spaces |
| title_fullStr | Strong Convergence Iterative Algorithms for Equilibrium Problems and Fixed Point Problems in Banach Spaces |
| title_full_unstemmed | Strong Convergence Iterative Algorithms for Equilibrium Problems and Fixed Point Problems in Banach Spaces |
| title_short | Strong Convergence Iterative Algorithms for Equilibrium Problems and Fixed Point Problems in Banach Spaces |
| title_sort | strong convergence iterative algorithms for equilibrium problems and fixed point problems in banach spaces |
| url | http://dx.doi.org/10.1155/2013/619762 |
| work_keys_str_mv | AT shenghuawang strongconvergenceiterativealgorithmsforequilibriumproblemsandfixedpointproblemsinbanachspaces AT shinminkang strongconvergenceiterativealgorithmsforequilibriumproblemsandfixedpointproblemsinbanachspaces |