Hlawka's functional inequality

Abstract

The paper is devoted to the functional inequality (called by us Hlawka’s functional inequality) f(x + y) + f(y + z) + f(x + z) ≤ f(x + y + z) + f(x) + f(y) + f(z) for the unknown mapping f defined on an Abelian group, on a linear space or on the real line. The study of the foregoing inequality is motivated by Hlawka’s inequality: x + y + y + z + x + z ≤ x + y + z + x + y + z , which in particular holds true for all x, y, z from a real or complex inner product space.