%0 Journal Article
%T Correspondence between spirallike functions and starlike functions
%A Yong Chan Kim
%A Toshiyuki Sugawa
%J Mathematics
%D 2010
%I arXiv
%X Let $\lambda$ be a real number with $-\pi/2<\lambda<\pi/2.$ In order to study $\lambda$-spirallike functions, it is natural to measure the angle according to $\lambda$-spirals. Thus we are led to the notion of $\lambda$-argument. This fits well the classical correspondence between $\lambda$-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.
%U http://arxiv.org/abs/1003.1566v1