On a generalization of a theorem of Levin and Stečkin and inequalities of the Hermite-Hadamard type

Abstract

We give new necessary and sufficient conditions for higher order convex ordering. These results generalize the Levin-Stečkin theorem (1960) on convex ordering. The obtained results can be useful in the study of the Hermite-Hadamard type inequalities and in particular inequalities between the quadrature operators.

arXiv comment12