Opuscula Mathematica
Opuscula Math. 31, no. 1 (), 15-26
Opuscula Mathematica

On strongly midconvex functions

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.
Mathematics Subject Classification: 26B25, 39B62.
Cite this article as:
Antonio Azócar, José Giménez, Kazimierz Nikodem, José Luis Sánchez, On strongly midconvex functions, Opuscula Math. 31, no. 1 (2011), 15-26, http://dx.doi.org/10.7494/OpMath.2011.31.1.15
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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