Existence and approximation for a solution of a generalized equilibrium problem on the dual space of a Banach space

In this paper, we first prove the existence of a solution for a generalized equilibrium problem with a bifunction defined on the dual space in a Banach space setting. Second, by the virtue of this result, we construct the hybrid projection method for solving a solution of a generalized equilibrium problem. Consequently, we establish the strong convergence theorem by using sunny generalized nonexpansive retraction in the dual of Banach spaces. MSC: 47H09, 47H10, 47J25.