Monotone Hybrid Methods for a Finite Family of Nonexpasive Multi-valued Maps and Equilibrium Problems

Abstract

In this paper, we introduce a new monotone hybrid iterative scheme for finding a common element of the set of common fixed points of a finite family of nonexpansive multivalued maps and the set of the solutions of the equilibrium problem in a Hilbert space. Moreover,we also introduce a new iterative scheme for finding a common fixed point of a finite family of nonexpansive multi-valued maps in a Banach space. Strong convergence theorem of the proposed iteration is established.