Starlikeness of certain analytic functions

Let f and g be analytic functions on the open unit disk of the complex plane with f/g belonging to the class \mathcal{P} of functions with positive real part consisting of functions p with p(0)=1 and \operatorname{Re} p(z)>0 or to its subclass consisting of functions p with |p(z)-1|<1. We... Show more