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

References

  1. J. Borwein, O. Giladi: Convex analysis on groups and semigroups, Math. Programming 168 (2018) 11–53.https://doi.org/10.1007/s10107-016-1010-xGoogle Scholar
  2. W. Jarczyk, M. Laczkovich: Convexity on Abelian groups, J. Convex Analysis 16 (2009) 33–48.https://doi.org/10.68381/jca16002Google Scholar

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 LLC.