VISCOSITY APPROXIMATION METHODS FOR EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS OF NONLINEAR SEMIGROUPS

Abstract

The purpose of this paper is to suggest and analyze a new iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a commutative family of nonexpansive mappings in a Hilbert space. Then we prove a strong convergence theorem which is connected with the results of Takahashi and Takahashi [13] and Yao and Noor [147]. Using this result, we obtain two corollaries which improve and extend their results.