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Throughout this paper, we introduce a new hybrid iterative algorithm for finding a common element of the set of common fixed points of a finite family of uniformly asymptotically nonexpansive semigroups and the set of solutions of an equilibrium problem in the framework of Hilbert spaces. We then prove the strong convergence theorem with respect to the proposed iterative algorithm. Our results in this paper extend and improve some recent known results.

advances in pure mathematics

Convergence Theorem of Hybrid Iterative Algorithm for Equilibrium Problems and Fixed Point Problems of Finite Families of Uniformly Asymptotically Nonexpansive Semigroups