Geometric subfamily of functions convex in some direction and Blaschke products
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914880069566464 |
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| author | Li, Liulan Ponnusamy, Saminthan |
| author_facet | Li, Liulan Ponnusamy, Saminthan |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14922 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric subfamily of functions convex in some direction and Blaschke products Li, Liulan Ponnusamy, Saminthan Complex Variables 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. |
| title | Geometric subfamily of functions convex in some direction and Blaschke products |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2407.14922 |