Convergence Theorems for Bregman K-Mappings and Mixed Equilibrium Problems in Reflexive Banach Spaces
Joint Authors
Source
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-09-18
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
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 { T i } i = 1 N .
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.
American Psychological Association (APA)
Ali, Bashir& Harbau, M. H.. 2016. Convergence Theorems for Bregman K-Mappings and Mixed Equilibrium Problems in Reflexive Banach Spaces. Journal of Function Spaces،Vol. 2016, no. 2016, pp.1-18.
https://search.emarefa.net/detail/BIM-1108616
Modern Language Association (MLA)
Ali, Bashir& Harbau, M. H.. Convergence Theorems for Bregman K-Mappings and Mixed Equilibrium Problems in Reflexive Banach Spaces. Journal of Function Spaces No. 2016 (2016), pp.1-18.
https://search.emarefa.net/detail/BIM-1108616
American Medical Association (AMA)
Ali, Bashir& Harbau, M. H.. Convergence Theorems for Bregman K-Mappings and Mixed Equilibrium Problems in Reflexive Banach Spaces. Journal of Function Spaces. 2016. Vol. 2016, no. 2016, pp.1-18.
https://search.emarefa.net/detail/BIM-1108616
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1108616