AN ITERATIVE METHOD FOR FINDING COMMON SOLUTIONS OF GENERALIZED MIXED EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS

Abstract

In this paper, we introduce an iterative method for finding a common element ofthe set of solutions of a generalized mixed equilibrium problem and the set of common fixedpoints of a finite family of nonexpansive mappings in a real Hilbert space. Then, we prove thatthe sequence converges strongly to a common element of the above two sets. Furthermore,we apply our result to prove three new strong convergence theorems in fixed point problems,mixed equilibrium problems, generalized equilibrium problems and equilibrium problems.