Abstract

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.

Author information

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Keywords

  • Minimax theorem
  • alternative theorem
  • convexlikeness
  • infsup-convexity
  • function spaces

Mathematics Subject Classification

46E15, 46E10, 26B25; 26D99

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Suggested citation

M. Bachir. “Some New Minimax Theorems for Generalized Convexity.” Journal of Convex Analysis 33 (2026), No. 1&2, 111–130. https://doi.org/10.68381/jca33007

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Published by Heldermann Verlag, 2026. Rights now held by Banach Press LLC.