
Journal of Convex Analysis 25 (2018), No. 3, 10331043 Copyright Heldermann Verlag 2018 Separation Problems in the Context of hConvexity 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 hconvexity extends the notion of classical convexity, using some nonnegative function h of the weights on the righthand side in the defining inequality. The aim of the present note is to show that nonconstant haffine 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 hconvexity may have only particular importance. Keywords: Convex functions, Jensenaffine functions, affine and convex separation. MSC: 39B82; 39B62, 26A51, 52A37 [ Fulltextpdf (104 KB)] for subscribers only. 