Subadditive functions and partial converses of Minkowski's and Mulholland's inequalities
Volume 143 / 1993
Fundamenta Mathematicae 143 (1993), 75-85
DOI: 10.4064/fm-143-1-75-85
Abstract
Let ϕ be an arbitrary bijection of $ℝ_+$. We prove that if the two-place function $ϕ^{-1}[ϕ (s)+ϕ (t)]$ is subadditive in $ℝ^2_+$ then $ϕ $ must be a convex homeomorphism of $ℝ_+$. This is a partial converse of Mulholland's inequality. Some new properties of subadditive bijections of $ℝ_+$ are also given. We apply the above results to obtain several converses of Minkowski's inequality.
