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.
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