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

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 $2$.

arXiv comment6 pages, no figures