In this paper, we review and unify some classes of generalized convex functions introduced by different authors to prove minimax results in infinite-dimensional spaces and show the relations between these classes. We list also for the most general class already introduced by Jeyakumar (Ref. 1) an elementary proof of a minimax result. The proof of this result uses only a finite-dimensional separa- tion theorem; although this minimax result was already presented by Neumann (Ref. 2) and independently by Jeyakumar (Ref. 1), we believe that the present proof is shorter and more transparent.

Journal of Optimization Theory and Applications
Erasmus Research Institute of Management

Frenk, J.B.G, & Kassay, G. (2002). Minimax results and finite-dimensional separation. Journal of Optimization Theory and Applications (Vol. 113, pp. 409–421). doi:10.1023/A:1014843327958