Correspondence between spirallike functions and starlike functions

Yong Chan Kim; Toshiyuki Sugawa

doi:10.1002/mana.201010020

Correspondence between spirallike functions and starlike functions

Yong Chan Kim, Toshiyuki Sugawa

INF - Computer and Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

Let λ be a real number with -π/2 < λ < π/2. In order to study λ-spirallike functions, it is natural to measure the angle according to λ-spirals. Thus we are led to the notion of λ-argument. This fits well the classical correspondence between λ-spirallike functions and starlike functions. Using this idea, we extend deep results of Pommerenke and Sheil-Small on starlike functions to spirallike functions. As an application, we solved a problem given by Hansen in 6.

Original language	English
Pages (from-to)	322-331
Number of pages	10
Journal	Mathematische Nachrichten
Volume	285
Issue number	2-3
DOIs	https://doi.org/10.1002/mana.201010020
Publication status	Published - 2012 Feb 1

Keywords

Hardy space
Logarithmic spiral
Spirallike (spiral-like) function
Starlike function

ASJC Scopus subject areas

Mathematics(all)

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10.1002/mana.201010020

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AU - Sugawa, Toshiyuki

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AB - Let λ be a real number with -π/2 < λ < π/2. In order to study λ-spirallike functions, it is natural to measure the angle according to λ-spirals. Thus we are led to the notion of λ-argument. This fits well the classical correspondence between λ-spirallike functions and starlike functions. Using this idea, we extend deep results of Pommerenke and Sheil-Small on starlike functions to spirallike functions. As an application, we solved a problem given by Hansen in 6.

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KW - Logarithmic spiral

KW - Spirallike (spiral-like) function

KW - Starlike function

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