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arXiv · 1003.1566

Correspondence between spirallike functions and starlike functions

Yong Chan Kim·Toshiyuki Sugawa
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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 1971.

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Yong Chan Kim, Toshiyuki Sugawa. 2010-03-08. Correspondence between spirallike functions and starlike functions. https://arxiv.org/abs/1003.1566

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