Minimax results and finite dimensional separation

In this paper we review and unify some of the classes of generalized convex functions introduced by different authors to prove minimax results in infinite dimensional spaces and show the relations between those classes. We also list for the most general class already introduced by Jeyakumar an elementary proof of a minimax result. The proof of this result only uses a finite dimensional separation theorem and although this minimax result is already presented by Neumann and independently Jeyakumar we believe that the present proof is shorter and more transparent.