Duality for Equilibrium Problems

We consider equilibrium problems in the framework of the formulation proposed by Blum and Oettli. We establish a new dual formulation for this equilibrium problem using the classical Fenchel conjugation, thus generalizing the classical convex duality theory for optimization problems. This work was begun when the first author was visiting the Instituto de Matemática y Ciencias Afines (Lima-Peru) in July 2002 and was finished when the second author was visiting the Centre de Recerca Matemàtica (Bellaterra-Spain) in September 2002.