A self-duality of strong starlikeness

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18 Citations (Scopus)

Abstract

In this note, we will show that a simply connected bounded domain D is strongly starlike of order α < 1 with respect to the origin if and only if so is D˅, where D˅ is the analytic inversion of the exterior of D, namely, D˅ = {w ∈ C: 1/w ∈ Ĉ\˅}. This fact neatly explains the relationship between some known properties of strongly starlike domains and provides several new characterizations for those domains.

Original languageEnglish
Pages (from-to)382-389
Number of pages8
JournalKodai Mathematical Journal
Volume28
Issue number2
DOIs
Publication statusPublished - 2005 Jan 1
Externally publishedYes

Keywords

  • logarithmic spiral
  • strongly starlike

ASJC Scopus subject areas

  • Mathematics(all)

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