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Converse Ohlin’s lemma for convex and strongly convex functions

Adamek Mirosław, Nikodem Kazimierz

Journal of Applied Analysis

2023

Vol. 29, nr 1

123--126

Theorems which are converse to the Ohlin lemma for convex and strongly convex functions are proved. New proofs of probabilistic characterizations of convex and strongly convex functions are presented.

On strongly midconvex functions

Azocar A., Gimenez J., Nikodem K., Sanchez J. L.

Opuscula Mathematica

2011

Vol. 31, no. 1

15-26

In this paper we collect some properties of strongly midconvex functions. First, counterparts of the classical theorems of Bernstein-Doetsch, Ostrowski and Sierpiński are presented. A version of Rod é support theorem for strongly midconvex functions and a Kuhn-type result on the relation between strongly midconvex functions and strongly t-convex functions are obtained. Finally, a connection between strong midconvexity and generalized convexity in the sense of Beckenbach is established