Dual equilibrium problems in reflexive Banach spaces

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