STRONG CONVERGENCE THEOREMS FOR FIXED POINT PROBLEMS AND EQUILIBRIUM PROBLEMS WITH APPLICATIONS

Abstract

In this paper, we present a new iterative algorithm for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of an equilibrium problem, and we prove the strong convergence theorems in Hilbert spaces.  We also apply our results to the convex minimization and variational inequality problems.  Our results extend and improve some recent results of Cai, Tang and Liu [Cai, Y., Tang, Y. and Liu, L.: Iterative algorithms for minimum-norm fixed point of nonexpansive mapping in Hilbert space. Fixed Point Theory Appl., 2012:49 (2012)] and others.