Equilibrium problem under various types of convexities in Banach space

Abstract

In this paper we establish the existence and uniqueness solution of the dual equilibrium problem on closed convex set. We give a link between the solutions set of equilibrium problem and its dual. The same link have also been established between invex equilibrium problem and its dual. For invex equilibrium problem, we have shown that the nonempty and boundedness of the solution sets imply the coercivity conditions of the bi-function. We have shown, how an equilibrium problem can be cast to a corresponding variational inequality problem for some special class of bi-functions.