Sharp radius of concavity for certain classes of analytic functions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910580781088768 |
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| author | Ahamed, Molla Basir Hossain, Rajesh |
| author_facet | Ahamed, Molla Basir Hossain, Rajesh |
| contents | Let $\mathcal{A}$ be the class of all analytic functions $f$ defined on the open unit disk $\mathbb{D}$ with the normalization $f(0)=0=f^{\prime}(0)-1$. This paper examines the radius of concavity for various subclasses of $\mathcal{A}$, namely $\mathcal{S}_0^{(n)}$, $\mathcal{K(α,β)}$, $\mathcal{\tilde{S^*}(β)}$, and $\mathcal{S}^*(α)$. It also presents results for various classes of analytic functions on the unit disk. All the radii are best possible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15544 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp radius of concavity for certain classes of analytic functions Ahamed, Molla Basir Hossain, Rajesh Complex Variables Primary 30C45, 30C55, 30C80 Let $\mathcal{A}$ be the class of all analytic functions $f$ defined on the open unit disk $\mathbb{D}$ with the normalization $f(0)=0=f^{\prime}(0)-1$. This paper examines the radius of concavity for various subclasses of $\mathcal{A}$, namely $\mathcal{S}_0^{(n)}$, $\mathcal{K(α,β)}$, $\mathcal{\tilde{S^*}(β)}$, and $\mathcal{S}^*(α)$. It also presents results for various classes of analytic functions on the unit disk. All the radii are best possible. |
| title | Sharp radius of concavity for certain classes of analytic functions |
| topic | Complex Variables Primary 30C45, 30C55, 30C80 |
| url | https://arxiv.org/abs/2408.15544 |