A generalization of convex functions via support properties

Abstract

AbstractWith respect to a given family of functionsF, a function is said to beF-convex, if it is supported, at each point, by some member ofF. For particular choices ofFone obtains the convex functions and the generalized convex functions in the sense of Beckenbach.F-convex functions are characterized and studied, retaining some essential results of classical convexity.