Convergence Theorems for Bregman K-Mappings and Mixed Equilibrium Problems in Reflexive Banach Spaces
We introduce a new mixed equilibrium problem with a relaxed monotone mapping in a reflexive Banach space and prove the existence of solution of the equilibrium problem. Using Bregman distance, we introduce the concept of Bregman K-mapping for a finite family of Bregman quasiasymptotically nonexpansi...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2016-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/5161682 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850166668174557184 |
|---|---|
| author | Bashir Ali M. H. Harbau |
| author_facet | Bashir Ali M. H. Harbau |
| author_sort | Bashir Ali |
| collection | DOAJ |
| description | We introduce a new mixed equilibrium problem with a relaxed monotone mapping in a reflexive Banach space and prove the existence of solution of the equilibrium problem. Using Bregman distance, we introduce the concept of Bregman K-mapping for a finite family of Bregman quasiasymptotically nonexpansive mappings and show the fixed point set of the Bregman K-mapping is the set of common fixed points of {Ti}i=1N. Using the Bregman K-mapping, we introduce an iterative sequence for finding a common point in the set of a common fixed points of the finite family of Bregman quasiasymptotically nonexpansive mappings and the set of solutions of some mixed equilibrium problems. Strong convergence of the iterative sequence is proved. Our results generalise and improve many recent results in the literature. |
| format | Article |
| id | doaj-art-e336ca2b967d4f4ba421fb635c43cc43 |
| institution | OA Journals |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-e336ca2b967d4f4ba421fb635c43cc432025-08-20T02:21:23ZengWileyJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/51616825161682Convergence Theorems for Bregman K-Mappings and Mixed Equilibrium Problems in Reflexive Banach SpacesBashir Ali0M. H. Harbau1Department of Mathematical Sciences, Bayero University, Kano, NigeriaDepartment of Mathematical Sciences, Bayero University, Kano, NigeriaWe introduce a new mixed equilibrium problem with a relaxed monotone mapping in a reflexive Banach space and prove the existence of solution of the equilibrium problem. Using Bregman distance, we introduce the concept of Bregman K-mapping for a finite family of Bregman quasiasymptotically nonexpansive mappings and show the fixed point set of the Bregman K-mapping is the set of common fixed points of {Ti}i=1N. Using the Bregman K-mapping, we introduce an iterative sequence for finding a common point in the set of a common fixed points of the finite family of Bregman quasiasymptotically nonexpansive mappings and the set of solutions of some mixed equilibrium problems. Strong convergence of the iterative sequence is proved. Our results generalise and improve many recent results in the literature.http://dx.doi.org/10.1155/2016/5161682 |
| spellingShingle | Bashir Ali M. H. Harbau Convergence Theorems for Bregman K-Mappings and Mixed Equilibrium Problems in Reflexive Banach Spaces Journal of Function Spaces |
| title | Convergence Theorems for Bregman K-Mappings and Mixed Equilibrium Problems in Reflexive Banach Spaces |
| title_full | Convergence Theorems for Bregman K-Mappings and Mixed Equilibrium Problems in Reflexive Banach Spaces |
| title_fullStr | Convergence Theorems for Bregman K-Mappings and Mixed Equilibrium Problems in Reflexive Banach Spaces |
| title_full_unstemmed | Convergence Theorems for Bregman K-Mappings and Mixed Equilibrium Problems in Reflexive Banach Spaces |
| title_short | Convergence Theorems for Bregman K-Mappings and Mixed Equilibrium Problems in Reflexive Banach Spaces |
| title_sort | convergence theorems for bregman k mappings and mixed equilibrium problems in reflexive banach spaces |
| url | http://dx.doi.org/10.1155/2016/5161682 |
| work_keys_str_mv | AT bashirali convergencetheoremsforbregmankmappingsandmixedequilibriumproblemsinreflexivebanachspaces AT mhharbau convergencetheoremsforbregmankmappingsandmixedequilibriumproblemsinreflexivebanachspaces |