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Currently displaying 1 – 5 of 5

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Properties of a function of E. Marczewski

T. Świątkowski — 1978

Fundamenta Mathematicae

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

T. Świątkowski — 1963

Fundamenta Mathematicae

On some generalization of the notion of asymmetry of functions

T. Świątkowski — 1967

Colloquium Mathematicae

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

T. Świątkowski — 1967

Colloquium Mathematicae

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

J. Matkowski; T. Świątkowski — 1993

Fundamenta Mathematicae

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.

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