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We introduce a new hybrid iterative scheme for finding a common element of the setof common fixed points of two countable families of relatively quasi-nonexpansive mappings, the setof the variational inequality for an α-inverse-strongly monotone operator, the set of solutions of thegeneralized mixed equilibrium problem and zeros of a maximal monotone operator in the framework of areal Banach space. We obtain a strong convergence theorem for the sequences generated by this processin a 2 uniformly convex and uniformly smooth Banach space. The results presented in this paper improveand extend some recent results

abstract and applied analysis

A Hybrid Iterative Scheme for a Maximal Monotone Operator and Two Countable Families of Relatively Quasi-Nonexpansive Mappings for Generalized Mixed Equilibrium and Variational Inequality Problems