Quasiconformal extension of meromorphic functions with nonzero pole

B. Bhowmik, G. Satpati, T. Sugawa

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

In this note, we consider meromorphic univalent functions f(z) in the unit disc with a simple pole at z = p ∈ (0, 1) which have a k-quasiconformal extension to the extended complex plane ℂ, where 0 ≤ k < 1. We denote the class of such functions by Σk(p). We first prove an area theorem for functions in this class. Next, we derive a sufficient condition for meromorphicT5 functions in the unit disc with a simple pole at z = p ∈ (0, 1) to belong to the class Σk(p). Finally, we give a convolution property for functions in the class Σk(p).

Original languageEnglish
Pages (from-to)2593-2601
Number of pages9
JournalProceedings of the American Mathematical Society
Volume144
Issue number6
DOIs
Publication statusPublished - 2016 Jun

Keywords

  • Convolution
  • Quasiconformal map

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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