Sharp Lipschitz Constants for the Distance Ratio Metric

  • Slavko Simić
  • Matti Vuorinen
  • Gendi Wang

Abstract

We study expansion/contraction properties of some common classes of mappings of the Euclidean space $\mathsf{R}^n$, $n\ge 2$, with respect to the distance ratio metric. The first main case is the behavior of Möbius transformations of the unit ball in $\mathsf{R}^n$ onto itself. In the second main case we study the polynomials of the unit disk onto a subdomain of the complex plane. In both cases sharp Lipschitz constants are obtained.
Published
2015-03-04
How to Cite
Simić, S., Vuorinen, M., & Wang, G. (2015). Sharp Lipschitz Constants for the Distance Ratio Metric. MATHEMATICA SCANDINAVICA, 116(1), 86-103. https://doi.org/10.7146/math.scand.a-20452
Section
Articles