The distance ratio metric on some parts of $\mathbb C$ plane

Slavko Simic

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arXiv · 1401.8014

The distance ratio metric on some parts of $\mathbb C$ plane

Slavko Simic

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Abstract

We prove a generalization for some $\mathbb C$ domains of Gehring - Palka theorem on Moebius transformations regarding the distance ratio metric. Namely, we show that this theorem is valid for arbitrary holomorphic mappings $f : H \to H$ or $f : D \to D$ with the same Lipschitz constant $2$.

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Slavko Simic. 2014-01-30. The distance ratio metric on some parts of $\mathbb C$ plane. https://arxiv.org/abs/1401.8014

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