Opuscula Math. 31, no. 1 (2011), 15-26
http://dx.doi.org/10.7494/OpMath.2011.31.1.15
Opuscula Mathematica
On strongly midconvex functions
Antonio Azócar
José Giménez
Kazimierz Nikodem
José Luis Sánchez
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.
- Antonio Azócar
- Universidad Nacional Abierta, Departamento de Matemáticas, Caracas, Venezuela
- José Giménez
- Universidad de los Andes, Facultad de Ciencias, Departamento de Matemáticas, Mérida, Venezuela
- Kazimierz Nikodem
- University of Bielsko-Biała, Department of Mathematics and Computer Science, ul. Willowa 2, 43-309 Bielsko-Biała, Poland
- José Luis Sánchez
- Universidad Central de Venezuela, Escuela de Matemáticas, Caracas, Venezuela
- Received: 2010-03-04.
- Revised: 2010-05-05.
- Accepted: 2010-06-06.
