Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Convex functions
  • Jensen-affine functions
  • affine and convex separation

Mathematics Subject Classification

39B82; 39B62, 26A51, 52A37

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Suggested citation

M. Bessenyei, E. Pénzes. “Separation Problems in the Context of h-Convexity.” Journal of Convex Analysis 25 (2018), No. 3, 1033–1043. https://doi.org/10.68381/jca25066

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Published by Heldermann Verlag, 2018. Rights now held by Banach Press LLC.