The Bohr Phenomenon for analytic functions on simply connected domains
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866913027367895040 |
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| author | Ahamed, Molla Basir Allu, Vasudevarao Halder, Himadri |
| author_facet | Ahamed, Molla Basir Allu, Vasudevarao Halder, Himadri |
| contents | In this paper, we investigate the Bohr phenomenon for the class of analytic functions defined on the simply connected domain
\begin{equation*}
Ω_γ=\bigg\{z\in\mathbb{C} : \bigg|z+\fracγ{1-γ}\bigg|<\frac{1}{1-γ}\bigg\}\;\; \text{for}\;\; 0\leq γ<1.
\end{equation*} We study improved Bohr radius, Bohr-Rogosinski radius and refined Bohr radius for the class of analytic functions defined in $ Ω_γ $, and obtain several sharp results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_13890 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The Bohr Phenomenon for analytic functions on simply connected domains Ahamed, Molla Basir Allu, Vasudevarao Halder, Himadri Complex Variables 30C45, 30C50, 30C80 In this paper, we investigate the Bohr phenomenon for the class of analytic functions defined on the simply connected domain \begin{equation*} Ω_γ=\bigg\{z\in\mathbb{C} : \bigg|z+\fracγ{1-γ}\bigg|<\frac{1}{1-γ}\bigg\}\;\; \text{for}\;\; 0\leq γ<1. \end{equation*} We study improved Bohr radius, Bohr-Rogosinski radius and refined Bohr radius for the class of analytic functions defined in $ Ω_γ $, and obtain several sharp results. |
| title | The Bohr Phenomenon for analytic functions on simply connected domains |
| topic | Complex Variables 30C45, 30C50, 30C80 |
| url | https://arxiv.org/abs/2011.13890 |