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Sharp Lipschitz Constants for the Distance Ratio Metric

Slavko Simić, Matti Vuorinen, Gendi Wang


We study expansion/contraction properties of some common classes of mappings of the Euclidean space $\mathsf{R}^n$, $n\ge 2$, with respect to the distance ratio metric. The first main case is the behavior of Möbius transformations of the unit ball in $\mathsf{R}^n$ 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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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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