Subadditive functions and partial converses of Minkowski's and Mulholland's inequalities
Fundamenta Mathematicae, Tome 143 (1993) no. 1, pp. 75-85
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
subadditive function, homeomorphisms of $ℝ_+$, Mulholland's inequality, convex function, iteration, measure space, the converse of Minkowski's inequality
Affiliations des auteurs :
Janusz Matkowski 1 ; Tadeusz Świa̧tkowski 2
@article{10_4064_fm_143_1_75_85,
author = {Janusz Matkowski and Tadeusz \'Swia̧tkowski},
title = {Subadditive functions and partial converses of {Minkowski's} and {Mulholland's} inequalities},
journal = {Fundamenta Mathematicae},
pages = {75--85},
year = {1993},
volume = {143},
number = {1},
doi = {10.4064/fm-143-1-75-85},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-143-1-75-85/}
}
TY - JOUR AU - Janusz Matkowski AU - Tadeusz Świa̧tkowski TI - Subadditive functions and partial converses of Minkowski's and Mulholland's inequalities JO - Fundamenta Mathematicae PY - 1993 SP - 75 EP - 85 VL - 143 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4064/fm-143-1-75-85/ DO - 10.4064/fm-143-1-75-85 LA - en ID - 10_4064_fm_143_1_75_85 ER -
%0 Journal Article %A Janusz Matkowski %A Tadeusz Świa̧tkowski %T Subadditive functions and partial converses of Minkowski's and Mulholland's inequalities %J Fundamenta Mathematicae %D 1993 %P 75-85 %V 143 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4064/fm-143-1-75-85/ %R 10.4064/fm-143-1-75-85 %G en %F 10_4064_fm_143_1_75_85
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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