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

100%

Matkowski J., Świątkowski T.

Fundamenta Mathematicae

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1993

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tom 143

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nr 1

75-85

EN

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.

2

Sur la transformation d'une fonction mesurable en une fonction sommable

70%

Świątkowski T.

Fundamenta Mathematicae

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1963

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tom 52

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nr 1

1-13

3

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On some generalization of the notion of asymmetry of functions

60%

Świątkowski T.

Colloquium Mathematicum

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1967

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tom 17

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nr 1

77-91

4

On the holomorphism of the integral with respect to a complex parameter

60%

Świątkowski T.

Colloquium Mathematicum

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1967

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tom 16

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nr 1

61-65

5

Properties of a function of E. Marczewski

50%

Świątkowski T.

Fundamenta Mathematicae

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1978

|

tom 100

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nr 1

45-49

Ograniczanie wyników

3 Fundamenta Mathematicae

2 Colloquium Mathematicum

5 Świątkowski T.

1 Matkowski J.

1 1993

1 1978

2 1967

1 1963

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

Sur la transformation d'une fonction mesurable en une fonction sommable

On some generalization of the notion of asymmetry of functions

On the holomorphism of the integral with respect to a complex parameter

Properties of a function of E. Marczewski