Abstract

In a recent paper we have introduced the concept of (ω, t)-convexity and ω-convexity as a natural generalization of the concept of usual convexity, strong-convexity, approximate-convexity, Wright-convexity and many others. The main result of this paper gives a necessary and sufficient condition on ω under which we can separate an (ω, t)-convex (ω-convex) function and (ω, t)-concave (ω-concave) function by an (ω, t)-affine map (ω-affine map). It turns out that in both cases ω has to satisfy some functional equation. We solve these functional equations in the most frequently appearing form of the map ω. Several applications of the main results are also given.

Author information

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Keywords

  • Convexity
  • t-convexity
  • midpoint-convexity
  • separation theorem

Mathematics Subject Classification

26A51, 26B25, 39B62, 46C15, 52A41

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Suggested citation

A. Olbryś. “A Sandwich Theorem for Generalized Convexity and Applications.” Journal of Convex Analysis 26 (2019), No. 3, 887–902. https://doi.org/10.68381/jca26047

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Published by Heldermann Verlag, 2019. Rights now held by Banach Press LLC.