Let be a real Banach space and closed, convex and nonempty. A mapping is said to be -inverse strongly monotone if there exists such that
The authors introduce an iterative process of the type:
converging strongly to a common element of the set of common fixed points of the countably infinite family of closed relatively quasi-nonexpensive mappings, the solution set of a generalized equilibrium problem and the solution set of a variational inequality problem for a -inverse strongly monotone mapping in Banach spaces. The theorems of the paper improve, generalize, unify and extend several known results.