Strong Convergence Theorems for Quasi‐Bregman Nonexpansive Mappings in Reflexive Banach Spaces

Mohammed Ali Alghamdi, Naseer Shahzad and Habtu Zegeye

Journal of Applied Mathematics, 2014, vol. 2014, issue 1

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.

Date: 2014
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https://doi.org/10.1155/2014/580686

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2014:y:2014:i:1:n:580686

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