Journal of Convex Analysis 33 (2026), No. 1&2, 111--130
Copyright Heldermann Verlag 2026
Some New Minimax Theorems for Generalized Convexity
Mohammed Bachir
Laboratoire SAMM 4543, Université Paris 1 Panthéon-Sorbonne, Paris, France
Mohammed.Bachir@univ-paris1.fr
The aim of this article is to establish new two-functions minimax inequalities extending classical results such as Simons' minimax theorem. Our results will be proved in a non-compact setting. We also prove, under general conditions, that the one-function minimax equality is in fact equivalent to the well known Simons inequality. Some applications will be given.
Keywords: Minimax theorem, alternative theorem, convexlikeness, infsup-convexity, function spaces.
MSC: 46E15, 46E10, 26B25; 26D99.
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