Improvements of certain results of the class $\mathcal{S}$ of univalent functions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912127713804288 |
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| author | Obradović, Milutin Tuneski, Nikola |
| author_facet | Obradović, Milutin Tuneski, Nikola |
| contents | For $f\in \mathcal{S}$, the class univalent functions in the unit disk $\mathbb{D}$ and given by $f(z)=z+\sum_{n=2}^{\infty} a_n z^n$ for $z\in \mathbb{D}$, we improve previous bounds for the second and third Hankel determinants in case when either $a_2=0,$ or $a_3=0$. We also improve an upper bound for the coefficient difference $|a_4|-|a_3|$ when $f\in \mathcal{S}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13102 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Improvements of certain results of the class $\mathcal{S}$ of univalent functions Obradović, Milutin Tuneski, Nikola Complex Variables 30C45, 30C50, 30C55 For $f\in \mathcal{S}$, the class univalent functions in the unit disk $\mathbb{D}$ and given by $f(z)=z+\sum_{n=2}^{\infty} a_n z^n$ for $z\in \mathbb{D}$, we improve previous bounds for the second and third Hankel determinants in case when either $a_2=0,$ or $a_3=0$. We also improve an upper bound for the coefficient difference $|a_4|-|a_3|$ when $f\in \mathcal{S}$. |
| title | Improvements of certain results of the class $\mathcal{S}$ of univalent functions |
| topic | Complex Variables 30C45, 30C50, 30C55 |
| url | https://arxiv.org/abs/2411.13102 |