The equivalence of discrete convexity and the classical definition of convexity

Abstract

This article presents a proof of the fact that the classical definition of convexity of nondecreasing (increasing) first forward differences for discrete univariate functions is actually a special case of the concept of discrete convexity for functions defined on a discrete space. Consequently proving the discrete convexity of separable functions is simplified and becomes simply showing each univariate function is convex in the classical sense. An illustrative example is provided.