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arXiv · 2309.14732

Schwarzian Norm Estimate for Functions in Generalized Robertson Class

Sanjit Pal
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Abstract

Let $\mathcal{A}$ be the class of analytic functions $f$ in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$ with the normalized conditions $f(0)=0$, $f'(0)=1$. For $-π/2<α<π/2$ and $0\le β<1$, let $\mathcal{S}_α(β)$ be the subclass of $\mathcal{A}$ consisting of functions $f$ that satisfy the relation $${\rm Re\,} \left\{e^{iα}\left(1+\frac{zf''(z)}{f'(z)}\right)\right\}>β\cosα\quad\text{for}~z\in\mathbb{D}.$$ In the present study, we will compute the sharp estimate of the pre-Schwarzian and Schwarzian norms for functions in $\mathcal{S}_α(β)$.

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Sanjit Pal. 2023-09-26. Schwarzian Norm Estimate for Functions in Generalized Robertson Class. https://arxiv.org/abs/2309.14732

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