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Journal of Convex Analysis 31 (2024), No. 1, 297--304
Copyright Heldermann Verlag 2024

Jensen Convex Functions on Semigroups

Marcin Balcerowski
Sosnowiec, Poland

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.

Keywords: Jensen convex function, Jensen convex set, semigroup.

MSC: 26A51, 20M10.

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