SHRINKING PROJECTION METHOD OF PROXIMAL-TYPE FOR A GENERALIZED EQUILIBRIUM PROBLEM, A MAXIMAL MONOTONE OPERATOR AND A PAIR OF RELATIVELY NONEXPANSIVE MAPPINGS

The purpose of this paper is to introduce and consider a shrinking projection method of proximal-type for finding a common element of the set EP of solutions of a generalized equilibrium problem, the set F(S) boolean AND F((S) over tilde) of common fixed points of a pair of relatively nonexpansive mappings S, (S) over tilde and the set T(-1)0 of zeros of a maximal monotone operator T in a uniformly smooth and uniformly convex Banach space. It is proven that under appropriate conditions, the sequence generated by the shrinking projection method of proximal-type, converges strongly to some point in EP boolean AND F(S)boolean AND F((S) over tilde)boolean AND T(-1)0. This new result represents the improvement, generalization and development of the previously known ones in the literature.