A new iterative method for equilibrium problems and fixed point problems of nonexpansive mappings and monotone mappings

In this paper, we introduce a new iterative scheme for finding the common element of the set of fixed points of a nonexpansive mapping, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for α-inverse-strongly monotone mappings. We show that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions. This main theorem extends a recent result of Yao and Yao [Y. Yao, J.-C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Applied Mathematics and Computation 186 (2) (2007) 1551-1558].