Correspondence between spirallike functions and starlike functions

Let ? be a real number with -p/2 < ? < p/2. In order to study ?-spirallike functions, it is natural to measure the angle according to ?-spirals. Thus we are led to the notion of ?-argument. This fits well the classical correspondence between ?-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.