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

Matkowski, J.; Świątkowski, T.

Fundamenta Mathematicae, Tome 142 (1993), p. 75-85 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Publié le : 1993-01-01

Zbl 0796.39015

EUDML-ID : urn:eudml:doc:211993

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     author = {J. Matkowski and T. \'Swi\k atkowski},
     title = {Subadditive functions and partial converses of Minkowski's and Mulholland's inequalities},
     journal = {Fundamenta Mathematicae},
     volume = {142},
     year = {1993},
     pages = {75-85},
     zbl = {0796.39015},
     language = {en},
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Matkowski, J.; Świątkowski, T. Subadditive functions and partial converses of Minkowski's and Mulholland's inequalities. Fundamenta Mathematicae, Tome 142 (1993) pp. 75-85. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv143i1p75bwm/

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