Hybrid shrinking projection method for a generalized equilibrium problem, a maximal monotone operator and a countable family of relatively nonexpansive mappings

The purpose of this paper is to introduce and consider a hybrid shrinking projection method for finding a common element of the set EPEP of solutions of a generalized equilibrium problem, the set ⋂n=0∞F(Sn) of common fixed points of a countable family of relatively nonexpansive mappings {Sn}n=0∞ and the set T−10T−10 of zeros of a maximal monotone operator TT in a uniformly smooth and uniformly convex Banach space. It is proven that under appropriate conditions, the sequence generated by the hybrid shrinking projection method, converges strongly to some point in EP∩T−10∩(⋂n=0∞F(Sn)). This new result represents the improvement, complement and development of the previously known ones in the literature.