We study expansion/contraction properties of some common classes of mappings of the Euclidean space R-n, n >= 2, with respect to the distance ratio metric. The first main case is the behavior of Mobius transformations of the unit ball in 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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