Strong convergence theorems for quasi-Bregman nonexpansive mappings in reflexive banach spaces

Mohammed Ali Alghamdi, Naseer Shahzad, Habtu Zegeye

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number580686
JournalJournal of Applied Mathematics
Volume2014
DOIs
Publication statusPublished - Jan 1 2014

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Reflexive Banach Space
Banach spaces
Strong Theorems
Nonexpansive Mapping
Strong Convergence
Convergence Theorem
Common Fixed Point
Maximal Monotone Mapping
Relatively Nonexpansive Mapping
Nonlinear Mapping
Equilibrium Problem
Iterative Algorithm
Family
Zero
Theorem

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Cite this

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Strong convergence theorems for quasi-Bregman nonexpansive mappings in reflexive banach spaces. / Alghamdi, Mohammed Ali; Shahzad, Naseer; Zegeye, Habtu.

In: Journal of Applied Mathematics, Vol. 2014, 580686, 01.01.2014.

Research output: Contribution to journalArticle

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