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.

,
doi.org/10.1023/A:1014843327958, hdl.handle.net/1765/63055
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