Journal of Convex Analysis 34 (2027), No. 1, 019--025
Copyright Heldermann Verlag 2027
F-Convexity of Real Functions
Liping Yuan
(1) School of Mathematical Sciences, Hebei Normal University
(2) Hebei Research Center, Basic Discipline Pure Mathematics
(3) Hebei Key Laboratory, Computational Mathematics and Applications, Shijiazhuang, P. R. China
lpyuan@hebtu.edu.cn
Tudor Zamfirescu
(1) School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, P. R. China
(2) Fakultaet fuer Mathematik, Technical University, Dortmund, Germany
(3) Roumanian Academy, Bucharest, Roumania
tuzamfirescu@gmail.com
[Abstract-pdf]
Let $\cal F$ be a family of sets in $\mathbb{R}^d$. A set $M \subset \mathbb{R}^d$ is called $\cal F$-{\it convex} if for any points $x,y\in M$ there is a set $F\in \cal F$ such that $x,y\in F$ and $F\subset M$. A function $f: \mathbb{R}\rightarrow \mathbb{R}$ is called {\it $\cal F$-convex} if its epigraph is $\cal F$-convex. In this paper we investigate various $\cal F$-convexities for real functions.
Keywords: Rectangular and rq-convexity, C-convexity, Gamma-convexity, right convexity, real functions.
MSC: 52A10, 52A20.
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