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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.14922 |
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Table of Contents:
- Consider the family of locally univalent analytic functions $h$ in the unit disk $|z|<1$ with the normalization $h(0)=0$, $h'(0)=1$ and satisfying the condition $${\real} \left( \frac{z h''(z)}{αh'(z)}\right) <\frac{1}{2} ~\mbox{ for $z\in \ID$,} $$ where $0<α\leq1$. The aim of this article is to show that this family has several elegant properties such as involving Blaschke products, Schwarzian derivative and univalent harmonic mappings.