Halpern-Type Iterative Algorithm for an Infinite Family of Relatively Quasi-Nonexpansive Multivalued Mappings and Equilibrium Problem in Banach Spaces

Abstract

Strong convergence of a new iterative process based on the Shrinking projection method to a common element of the set of common fixed points of an infinite family of relatively quasi-nonexpansive multivalued mappings and the solution set of an equilibrium problem in a Banach space is established. Our results improved and extend the corresponding results announced by many others.

A New Multi-Step Iterative Algorithm for Approximating Common Fixed Points of a Finite Family of Multi-Valued Bregman Relatively Nonexpansive Mappings

“…Under some mild conditions on the parameters {α n } and {β i,n }, they prove that the sequence {x n } defined by Equation (3) converges strongly to a point p ∈ N i=1 F(T i ). On the other hand, Eslamian and Abkar [16] introduced a multi-step iterative process by a hybrid method as follows:…”