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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/2405.07997 |
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| _version_ | 1866909201074225152 |
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| author | Obradović, Milutin Tuneski, Nikola |
| author_facet | Obradović, Milutin Tuneski, Nikola |
| contents | It is well-known that the condition ${\operatorname{Re}} \left[1+\frac{zf''(z)}{f'(z)}\right]>0$, $z\in{\mathbb D}$, implies that $f$ is starlike function (i.e. convexity implies starlikeness). If the previous condition is not satisfied for every $z\in {\mathbb D}$, then it is possible to get new criteria for starlikeness by using $\left|\arg\left[α+\frac{zf''(z)}{f'(z)}\right]\right|$, $z\in{\mathbb D}$, where $α>1.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07997 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New criteria for starlikeness in the unit disc Obradović, Milutin Tuneski, Nikola Complex Variables 30C45, 30C50 It is well-known that the condition ${\operatorname{Re}} \left[1+\frac{zf''(z)}{f'(z)}\right]>0$, $z\in{\mathbb D}$, implies that $f$ is starlike function (i.e. convexity implies starlikeness). If the previous condition is not satisfied for every $z\in {\mathbb D}$, then it is possible to get new criteria for starlikeness by using $\left|\arg\left[α+\frac{zf''(z)}{f'(z)}\right]\right|$, $z\in{\mathbb D}$, where $α>1.$ |
| title | New criteria for starlikeness in the unit disc |
| topic | Complex Variables 30C45, 30C50 |
| url | https://arxiv.org/abs/2405.07997 |