Fixed points, coincidence points and maximal elements with applications to generalized equilibrium problems and minimax theory

In this paper, using a generalization of the Fan-Browder fixed point theorem, we obtain a new fixed point theorem for multivalued maps in generalized convex spaces from which we derive several coincidence theorems and existence theorems for maximal elements. Applications of these results to generalized equilibrium problems and minimax theory will be given in the last sections of the paper.