Abstract
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.
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Frenk, J., Kassay, G. Minimax Results and Finite-Dimensional Separation. Journal of Optimization Theory and Applications 113, 409–421 (2002). https://doi.org/10.1023/A:1014843327958
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DOI: https://doi.org/10.1023/A:1014843327958