Distance Ratio Metric on the Unit Disk

Slavko Simic

doi:10.24297/jam.v6i3.3662

Distance Ratio Metric on the Unit Disk

Authors

Slavko Simic Mathematical Institute SANU, Belgrade

DOI:

https://doi.org/10.24297/jam.v6i3.3662

Keywords:

Lipschitz constant, analytic functions

Abstract

We prove Lipschitz continuity of arbitrary analytic mapping f : D --> D regarding the distance ratio metric with the Lipschitz constant C = 2. This represents a generalization for the unit disk domain of Gehring - Palka theorem on Mobius transformations.

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Author Biography

Slavko Simic, Mathematical Institute SANU, Belgrade

Department of Mathematics

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Published

2014-02-22

How to Cite

Simic, S. (2014). Distance Ratio Metric on the Unit Disk. JOURNAL OF ADVANCES IN MATHEMATICS, 6(3), 1056–1060. https://doi.org/10.24297/jam.v6i3.3662