@Article{Azócar2011,
author = "Azócar, Antonio and Giménez, José and Nikodem, Kazimierz and Sánchez, José Luis",
title = "On strongly midconvex functions",
journal = "Opuscula Math.",
year = "2011",
volume = "31",
number = "1",
pages = "15--26",
doi = "http://dx.doi.org/10.7494/OpMath.2011.31.1.15",
url = "http://dx.doi.org/10.7494/OpMath.2011.31.1.15",
abstract = "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.",
keywords = "strongly convex functions, strongly midconvex functions, Bernstein-Doetsch-type theorem, Kuhn theorem, Rodé support theorem, Beckenbach convexity",
issn = "1232-9274"
}