Schwarzian Norm Estimate for Functions in Robertson Class

2023/07/18 by Ali, Md Firoz, Pal, Sanjit · 4 citations
#30C45 #30C55 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.08976

Abstract

Let A denote the class of analytic functions f in the unit disk \mathbbD=\z∈ℂ:|z|<1\ normalized by f(0)=0, f'(0)=1. For -π/2<α<π/2, let S_α be the subclass of A consisting of functions f that satisfy the relation \rm Re \e^iα(1+zf''(z)/f'(z))\>0 for z∈\mathbbD. In the present article, we determine the sharp estimate of the pre-Schwarzian and Schwarzian norms for functions in the class S_α.

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