Viscosity iteration method for generalized equilibrium problems and fixed point problems of finite family of nonexpansive mappings

In this paper, we introduce an iterative scheme for finding a common element of the set of solutions of generalized equilibrium problem and the set of common fixed point of family of nonexpansive mappings in a Hilbert space. We prove the strong convergence of viscosity iterative algorithm to common element of the set of generalized equilibrium problem and the set of common fixed point of family of nonexpansive mappings. The result improve the recent ones of Ceng and Yao (2008) [L.C. Ceng, J.C. Yao, Hybrid viscosity approximation schemes for equilibrium problems and fixed point problems of infinitely many nonexpansive mappings, Appl. Math. Comput. 198 (2008) 729-741].