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arXiv · 2307.08976

Schwarzian Norm Estimate for Functions in Robertson Class

Md Firoz Ali·Sanjit Pal
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Abstract

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

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Md Firoz Ali, Sanjit Pal. 2023-07-18. Schwarzian Norm Estimate for Functions in Robertson Class. https://arxiv.org/abs/2307.08976

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