Dual Equilibrium Problems in Reflexive Banach Spaces

The aim of this paper is to investigate the dual problem of a generalized equilibrium problem in the framework of a reflexive Banach space. By means of the Fenchel duality, we introduce the dual problem defined via the Fitzpatrick transform of the bifunction involved, that turns out to be an equilibrium problem itself in the dual space. We present conditions which entail the solvability of both primal and dual problems.