Schwarzian Norm Estimate for Functions in Generalized Robertson Class
| Autor: | Pal, Sanjit |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $-\pi/2<\alpha<\pi/2$ and $0\le \beta<1$, let $\mathcal{S}_{\alpha}(\beta)$ be the subclass of $\mathcal{A}$ consisting of functions $f$ that satisfy the relation $${\rm Re\,} \left\{e^{i\alpha}\left(1+\frac{zf''(z)}{f'(z)}\right)\right\}>\beta\cos{\alpha}\quad\text{for}~z\in\mathbb{D}.$$ In the present study, we will compute the sharp estimate of the pre-Schwarzian and Schwarzian norms for functions in $\mathcal{S}_{\alpha}(\beta)$. Comment: arXiv admin note: substantial text overlap with arXiv:2307.08976 |
| Databáze: | arXiv |
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