Convergence Theorem Based on a New Hybrid Projection Method for Finding a Common Solution of Generalized Equilibrium and Variational Inequality Problems in Banach Spaces

The purpose of this paper is to introduce a new hybrid projection method for finding a commonelement of the set of common fixed points of two relatively quasi-nonexpansive mappings, the set ofthe variational inequality for an -inverse-strongly monotone, and the set of solutions of the generalizedequilibrium problem in the framework of a real Banach space. We obtain a strong convergence theoremfor the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. Base on this result, we also get some new and interesting results. The results in this paper generalize,extend, and unify some well-known strong convergence results in the literature.