Abstract

Let F\cal F be a family of sets in Rd\mathbb{R}^d. A set M⊂RdM \subset \mathbb{R}^d is called F\cal F-convex if for any points x,y∈Mx,y\in M there is a set F∈FF\in \cal F such that x,y∈Fx,y\in F and F⊂MF\subset M. A function f:R→Rf: \mathbb{R}\rightarrow \mathbb{R} is called F\cal F-convex if its epigraph is F\cal F-convex. In this paper we investigate various F\cal F-convexities for real functions

Author information

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Liping Yuan

School of Mathematical Sciences, Hebei Normal University; Hebei Research Center of the Basic Discipline Pure Mathematics; Hebei International Joint Research Center for Mathematics and Interdisciplinary Science; Hebei Key Laboratory of Computational Mathematics and Applications; Shijiazhuang, P. R. China

lpyuan@hebtu.edu.cn

Tudor Zamfirescu

(1) School of Mathematical Sciences, Hebei Normal University, Hebei International Joint Research Center for Mathematics and Interdisciplinary Science, Shijiazhuang, P. R. China
(2) Fakultät für Mathematik, Technical University, Dortmund, Germany
(3) Roumanian Academy, Bucharest, Roumania

tuzamfirescu@gmail.com

Keywords

  • Rectangular and rq-convexity
  • C-convexity
  • Gamma-convexity
  • right convexity
  • real functions

Mathematics Subject Classification

52A10, 52A20

References

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Suggested citation

L. Yuan, T. Zamfirescu. “F-Convexity of Real Functions.” Journal of Convex Analysis 34 (2027), No. 1, 16–20. https://doi.org/10.68381/jca34002

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