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

ArticleOriginal scientific text

Title

Authors ¹, ²

Department of Mathematics, Technical University, Willowa 2, 43-309 Bielsko-Biała, Poland
Institute of Mathematics, Technical University, Al. Politechniki 11, 90-924 Łódź, Poland

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.

subadditive function, homeomorphisms of

ℝ_{+}

, Mulholland's inequality, convex function, iteration, measure space, the converse of Minkowski's inequality

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