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

Alghamdi, Mohammed Ali; Shahzad, Naseer; Zegeye, Habtu

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.

MATHEMATICS theorems; STOCHASTIC analysis; BANACH spaces; EQUILIBRIUM; PROBLEM solving

Journal of Applied Mathematics, 2014, p1

1110-757X

Academic Journal

10.1155/2014/580686