Lipschitz Continuity of the Distance Ratio Metric on the Unit Disk

Slavko Simic

For maps of analytic functions $f:D\to D,f(0)=a\in D)$, we prove their Lipschitz continuity regarding the distance ratio metric with a Lipschitz constant $C$ depending only on $a$. Question of the best possible $C=C(a)$ remains open.