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arXiv · 1202.6565

Sharp Lipschitz constants for the distance ratio metric

Slavko Simić·Matti Vuorinen·Gendi Wang
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Abstract

We study expansion/contraction properties of some common classes of mappings of the Euclidean space ${\mathbb R}^n, n\ge 2\,,$ with respect to the distance ratio metric. The first main case is the behavior of M\"obius transformations of the unit ball in ${\mathbb R}^n$ onto itself. In the second main case we study the polynomials of the unit disk onto a subdomain of the complex plane. In both cases sharp Lipschitz constants are obtained.

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Slavko Simić, Matti Vuorinen, Gendi Wang. 2012-02-29. Sharp Lipschitz constants for the distance ratio metric. https://arxiv.org/abs/1202.6565

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