Geodesic
Subadditive functions and partial converses of Minkowski's and Mulholland's inequalities
Janusz Matkowski1 ; Tadeusz Świa̧tkowski2
1Department of Mathematics Technical University Willowa 2 43-309 Bielsko-Biała, Poland
2Institute Of Mathematics Technical University Al. Politechniki 11 90-924 Łódź, Poland
Fundamenta Mathematicae, Tome 143 (1993) no. 1, pp. 75-85
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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.
DOI : 10.4064/fm-143-1-75-85
Keywords: subadditive function, homeomorphisms of $ℝ_+$, Mulholland's inequality, convex function, iteration, measure space, the converse of Minkowski's inequality

Janusz Matkowski  1   ; Tadeusz Świa̧tkowski  2

1 Department of Mathematics Technical University Willowa 2 43-309 Bielsko-Biała, Poland
2 Institute Of Mathematics Technical University Al. Politechniki 11 90-924 Łódź, Poland 
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Janusz Matkowski; Tadeusz Świa̧tkowski. Subadditive functions and partial converses of Minkowski's and Mulholland's inequalities. Fundamenta Mathematicae, Tome 143 (1993) no. 1, pp. 75-85. doi: 10.4064/fm-143-1-75-85

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