
Journal of Convex Analysis 26 (2019), No. 3, 887902 Copyright Heldermann Verlag 2019 A Sandwich Theorem for Generalized Convexity and Applications Andrzej Olbrys Institute of Mathematics, University of Silesia, 40007 Katowice, Poland andrzej.olbrys@us.edu.pl In a recent paper we have introduced the concept of (ω, t)convexity and ωconvexity as a natural generalization of the concept of usual convexity, strongconvexity, approximateconvexity, Wrightconvexity 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 (ωconvex) function and (ω, t)concave (ωconcave) function by an (ω, t)affine map (ωaffine 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. Keywords: Convexity, tconvexity, midpointconvexity, separation theorem. MSC: 26A51, 26B25, 39B62, 46C15, 52A41 [ Fulltextpdf (111 KB)] for subscribers only. 