F-Convexity of Real Functions

Abstract

Let F be a family of sets in Rd. A set M⊂Rd is called F-convex if for any points x,y∈M there is a set F∈F such that x,y∈F and F⊂M. A function f:R→R is called F-convex if its epigraph is F-convex. In this paper we investigate various F-convexities for real functions