Abstract
We introduce an iterative process for finding common fixed point of finite family of quasi-Bregman nonexpansive mappings which is a unique solution of some equilibrium problem.
Highlights
Let E be a real reflexive Banach space and C a nonempty subset of E
We introduce an iterative process for finding common fixed point of finite family of quasi-Bregman nonexpansive mappings which is a unique solution of some equilibrium problem
Let T : C → C be a map, a point x ∈ C is called a fixed point of T if Tx = x, and the set of all fixed points of T is denoted by F(T)
Summary
Let E be a real reflexive Banach space and C a nonempty subset of E. Takahashi [5] obtain weak and strong convergence theorems for finding a common element of the set of solutions of an equilibrium problem and set of fixed points of nonexpansive mapping in Hilbert space. Motivated and inspired by the above works, in this paper, we prove a new strong convergence theorem for finite family of quasi-Bregman nonexpansive mapping and system of equilibrium problem in a real Banach space.
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