Derivates, Approximate Derivates and Porosity Derivates of n-Convex Functions

Abstract

It is shown that if $f$ is $n$-convex then the four $n$th order Peano derivates of $f$ are respectively equal to the corresponding $n$th order approximate Peano derivates and the porosity Peano derivates of $f$. It is further shown that the same result holds for the de la Vall\'ee Poussin derivates, and the symmetric and unsymmetric Riemann derivates.