TY  - JOUR
ID  - Azócar2011
LB  - Azócar2011
AU  - Azócar, Antonio
AU  - Giménez, José
AU  - Nikodem, Kazimierz
AU  - Sánchez, José Luis
TI  - On strongly midconvex functions
ST  - On strongly midconvex functions
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2011
VL  - 31
IS  - 1
SP  - 15
EP  - 26
DO  - http://dx.doi.org/10.7494/OpMath.2011.31.1.15
UR  - http://dx.doi.org/10.7494/OpMath.2011.31.1.15
AB  - 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.
KW  - strongly convex functions
KW  - strongly midconvex functions
KW  - Bernstein-Doetsch-type theorem
KW  - Kuhn theorem
KW  - Rodé support theorem
KW  - Beckenbach convexity
SN  - 1232-9274
ER  -