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

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Matkowski J., Świątkowski T.

Fundamenta Mathematicae

1993

tom 143

nr 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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Matkowski J.

1 Świątkowski T.

1 1993

Wyniki wyszukiwania

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