On strongly midconvex functions

• Main Authors: Antonio Azócar, José Giménez, Kazimierz Nikodem, José Luis Sánchez
• Format: Article
• Language: English
• Published: AGH Univeristy of Science and Technology Press 2011-01-01
• Series: Opuscula Mathematica
• Subjects: strongly convex functions; strongly midconvex functions; Bernstein-Doetsch-type theorem; Kuhn theorem; Rodé support theorem; Beckenbach convexity
• Online Access: http://www.opuscula.agh.edu.pl/vol31/1/art/opuscula_math_3102.pdf
• ISSN: 1232-9274

In this paper we collect some properties of strongly midconvex functions. First, counterparts of the classical theorems of Bernstein-Doetsch, Ostrowski and Sierpinski are presented. A version of Rodé 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.