Abstract

We transfer some results concerning Jensen convex functions defined on linear topological spaces to Jensen convex functions defined on semigroups. We also show that the Bernstein-Doetsch theorem fails in some class of topological semigroups.

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Keywords

  • Jensen convex function
  • Jensen convex set
  • semigroup

Mathematics Subject Classification

26A51, 20M10

Suggested citation

M. Balcerowski. “Jensen Convex Functions on Semigroups.” Journal of Convex Analysis 31 (2024), No. 1, 297–304. https://doi.org/10.68381/jca31019

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Published by Heldermann Verlag, 2024. Rights now held by Banach Press.