Correspondence between spirallike functions and starlike functions

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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