Volume no :27, Issue no: 1, May

Journal of Mathematical Sciences: Advances and Applications

DISTANCE RATIO METRIC ON A HALF-PLANE

Author's: Slavko Simic
Pages: [43] - [48]
Received Date: January 29, 2014; Revised February 7, 2014
Submitted by:

Abstract

We prove Lipschitz continuity of an arbitrary holomorphic mapping regarding the distance ratio metric with the Lipschitz constant This represents a generalization for the upper half-plane domain of Gehring - Palka theorem on Möbius transformations. We also proved that the constant 2 is best possible.

Keywords

Lipschitz constant, holomorphic mapping, Schwartz-Pick lemma.