Discrete convexity built on differences (Q2452051)

The author studies a class of discrete convex functions that was introduced by using differences of values of functions at certain points. For real-valued two-dimensional functions this class is equal to the class of integrally convex functions. It is shown that in higher dimensions a \(C\)-laterally convex function is integrally convex. Since a \(C\)-laterally convex function is integrally convex, a local minimum is a global one.