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Recently, Colao et al. (J Math Anal Appl 344:340-352, 2008) introduced a hybrid viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a finite family of nonexpansive mappings in a real Hilbert space. In this paper, by combining Colao, Marino and Xu's hybrid viscosity approximation method and Yamada's hybrid steepest-descent method, we propose a hybrid iterative method for finding a common element of the set GMEP of solutions of a generalized mixed equilibrium problem and the set ∩N i=1 Fix (S i) of fixed points of a finite family of nonexpansive mappings {Si}N i = 1 in a real Hilbert space. We prove the strong convergence of the proposed iterative algorithm to an element of ∩N i=1 Fix (Si) ∩ GMEP, which is the unique solution of a variational inequality. © 2012 Ceng et al.

Hybrid iterative method for finding common solutions of generalized mixed equilibrium and fixed point problems