Journal of Convex Analysis 25 (2018), No. 3, 1033--1043
Copyright Heldermann Verlag 2018
Separation Problems in the Context of h-Convexity
Mihály Bessenyei
Institute of Mathematics, University of Debrecen, Pf. 400, 4002 Debrecen, Hungary
besse@science.unideb.hu
Evelin Pénzes
Institute of Mathematics, University of Debrecen, Pf. 400, 4002 Debrecen, Hungary
penzesevelyn@gmail.com
The concept of h-convexity extends the notion of classical convexity, using some nonnegative function h of the weights on the right-hand side in the defining inequality. The aim of the present note is to show that nonconstant h-affine functions appear only in the classical convexity case. Affine and convex separation problems are also studied, without any further restrictions on h. The obtained results suggest that, in view of Convex Geometry or Convex Analysis, the notion of h-convexity may have only particular importance.
Keywords: Convex functions, Jensen-affine functions, affine and convex separation.
MSC: 39B82; 39B62, 26A51, 52A37
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