A self-duality of strong starlikeness

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Author(s)

    • Sugawa Toshiyuki
    • DEPARTMENT OF MATHEMATICS GRADUATE SCHOOL OF SCIENCE HIROSHIMA UNIVERSITY

Abstract

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

Journal

  • Kodai Mathematical Journal

    Kodai Mathematical Journal 28(2), 382-389, 2005

    Department of Mathematics, Tokyo Institute of Technology

Codes

  • NII Article ID (NAID)
    130003574499
  • Text Lang
    ENG
  • ISSN
    0386-5991
  • Data Source
    J-STAGE 
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