%0 Journal Article
%T On strongly midconvex functions
%A Antonio Az¨®car
%A Jos¨¦ Gim¨¦nez
%A Kazimierz Nikodem
%A Jos¨¦ Luis S¨˘nchez
%J Opuscula Mathematica
%D 2011
%I AGH University of Science and Technology
%X 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 Rod¨¦ 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.
%K strongly convex functions
%K strongly midconvex functions
%K Bernstein-Doetsch-type theorem
%K Kuhn theorem
%K Rod¨¦ support theorem
%K Beckenbach convexity
%U http://www.opuscula.agh.edu.pl/vol31/1/art/opuscula_math_3102.pdf