In the present work we deal with set-valued equilibrium problems for which we provide sufficient conditions for the existence of a solution. The conditions that we consider are imposed not on the whole domain, but rather on a self segment-dense subset of it, a special type of dense subset. As an application, we obtain a generalized Debreu-Gale-Nikaido type theorem, with a considerable weakned W...

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.