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

Volume 143 / 1993

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


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.


  • Janusz MatkowskiDepartment of Mathematics
    Technical University
    Willowa 2
    43-309 Bielsko-Biała, Poland
  • Tadeusz Świa̧tkowskiInstitute Of Mathematics
    Technical University
    Al. Politechniki 11
    90-924 Łódź, Poland

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