The Hornich-Hlawka functional inequality for functions with positive differences

Abstract

We analyze the role played by $n$-convexity for the fulfillment of a series of linear functional inequalities that extend the Hornich-Hlawka functional inequality, $f\left(x\right)+f\left(y\right)+f\left(z\right)+f\left(x+y+z\right)\ge f\left(x+y\right)+f\left(y+z\right)+f\left(z+x\right)+f(0),$ including extensions to the case of positive operators.

20 pages