Quasiconformal extension of strongly spirallike functions

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5 Citations (Scopus)

Abstract

We show that a strongly λ-spirallike function of order α can be extended to a sin(πα/2)-quasiconformal automorphism of the complex plane for -π/2 < λ < π/2 and 0 < α < 1 with {pipe} λ{pipe} < πα/2. Towards the proof we provide several geometric characterizations of a strongly λ-spirallike domain of order α. We also give a concrete form of the mapping function of the standard strongly λ-spirallike domain Uλ,αof order α. A key tool of the present study is the notion of λ-argument, which was developed by Y. C. Kim and the author [5].

Original languageEnglish
Pages (from-to)19-30
Number of pages12
JournalComputational Methods and Function Theory
Volume12
Issue number1
DOIs
Publication statusPublished - 2012 Jan 1

Keywords

  • Logarithmic spiral
  • Quasiconformal mapping
  • Spirallike (spiral-like) function

ASJC Scopus subject areas

  • Analysis
  • Computational Theory and Mathematics
  • Applied Mathematics

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