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Correspondence between spirallike functions and starlike functions

✍ Scribed by Yong Chan Kim; Toshiyuki Sugawa

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
131 KB
Volume
285
Category
Article
ISSN
0025-584X

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✦ Synopsis

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.

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