Schwarzian norm estimate for functions in Robertson class

Abstract

Let A denote the class of analytic functions f in the unit disk D={z∈C:|z|<1} normalized by f(0)=0, f′(0)=1. For −π/2<α<π/2, let Sα be the subclass of A consisting of functions f that satisfy the relation Re{eiα(1+zf″(z)/f′(z))}>0 for z∈D. In the present article, we determine the sharp estimate of the pre-Schwarzian and Schwarzian norms for functions in the class Sα.