Article ID Journal Published Year Pages File Type
4623803 Journal of Mathematical Analysis and Applications 2006 14 Pages PDF
Abstract

The problem of establishing inequalities of the Hermite–Hadamard type for convex functions on n-dimensional convex bodies translates into the problem of finding appropriate majorants of the involved random vector for the usual convex order. We present two results of partial generality which unify and extend the most part of the multidimensional Hermite–Hadamard inequalities existing in the literature, at the same time that lead to new specific results. The first one fairly applies to the most familiar kinds of polytopes. The second one applies to symmetric random vectors taking values in a closed ball for a given (but arbitrary) norm on Rn. Related questions, such as estimates of approximation and extensions to signed measures, also are briefly discussed.

Related Topics
Physical Sciences and Engineering Mathematics Analysis