On a generalization of a theorem of Levin and Steckin 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-Steckin 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.
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