Geodesic
The Bohr phenomenon for analytic functions on shifted disks
Molla Basir Ahamed1 ; Vasudevarao Allu1 ; Himadri Halder1
1Indian Institute of Technology Bhubaneswar, School of Basic Science
Annales Fennici Mathematici, Tome 47 (2022) no. 1, pp. 103-120

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In this paper, we investigate the Bohr phenomenon for the class of analytic functions defined on the simply connected domain $\Omega_{\gamma}=\bigg\{z\in\mathbb{C} \colon \bigg|z+\frac{\gamma}{1-\gamma}\bigg|<\frac{1}{1-\gamma}\bigg\}$ for $0\leq \gamma<1.$ We study improved Bohr radius, Bohr-Rogosinski radius and refined Bohr radius for the class of analytic functions defined in $\Omega_{\gamma}$, and obtain several sharp results.
DOI : 10.54330/afm.112561
Keywords: Simply connected domain, bounded analytic functions, improved Bohr radius, Bohr-Rogosinski radius, refined Bohr radius and Bohr inequality

Molla Basir Ahamed  1   ; Vasudevarao Allu  1   ; Himadri Halder  1

1 Indian Institute of Technology Bhubaneswar, School of Basic Science 
Molla Basir Ahamed; Vasudevarao Allu; Himadri Halder. The Bohr phenomenon for analytic functions on shifted disks. Annales Fennici Mathematici, Tome 47 (2022) no. 1, pp. 103-120. doi: 10.54330/afm.112561
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