Hybrid Proximal-Point Methods for Systems of Generalized Equilibrium Problems and Maximal Monotone Operators in Banach Spaces

In this paper, by using Bregman’s technique, we introduce and study the hybrid proximal-point methods for finding a common element of the set of solutions to a system of generalized equilibrium Problems and zeros of a finite family of maximal monotone operators in reflexive Banach spaces. Strong convergence results of the proposed hybrid proximal-point algorithms are also established under some suitable conditions. As applications, the existence of solutions for a class of bilevel variational inequalities are established and some numerical examples are reported. Key–Words: Equilibrium problem, maximal monotone operator, bilevel variational inequalities, Bregman distance, Bregman projection, totally convex function, Legendre function.