Sharp Lipschitz constants for the distance ratio metric

2012/02/29 by Slavko Simić, Simić, Slavko, Matti Vuorinen +3 · 1 citation
Mathematics · #30C20 #51M10 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:30C20 #msc:51M10

paper · pdf · doi:10.48550/arxiv.1202.6565

14 pages

arxiv created 2013/07/10 · arxiv updated 2013/07/11

Abstract

We study expansion/contraction properties of some common classes of mappings of the Euclidean space \mathbb Rⁿ, n≥ 2 , with respect to the distance ratio metric. The first main case is the behavior of Möbius transformations of the unit ball in \mathbb Rⁿ 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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