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# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Subadditive functions and partial converses of Minkowski's and Mulholland's inequalities

### Tom 143 / 1993

Fundamenta Mathematicae 143 (1993), 75-85 DOI: 10.4064/fm-143-1-75-85

#### Streszczenie

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.

#### Autorzy

• Janusz MatkowskiDepartment of Mathematics
Technical University
Willowa 2
43-309 Bielsko-Biała, Poland