On the integral representation and the Ra\c{s}a, Jensen and Hermite-Hadamard inequalities for box-$(n_1,\ldots, n_d)$-convex functions

Abstract

We give the integral representation of box-$(n_1,\ldots, n_d)$-convex fun\-ctions, which are a generalization of Popoviciu's $n$-convex and box-$(m,n)$-convex functions. Based on this integral representation, we obtain the Ra\c{s}a, Jensen and Hermite-Hadamard inequalities for these functions. We extend the results obtained by S. G. Gal, C. P. Niculescu, B. Gavrea, I. Gavrea, A. Komisarski, T. Rajba and T. Popoviciu.

Locations

• arXiv (Cornell University) - View - PDF