The Bohr Phenomenon for analytic functions on simply connected domains

Abstract

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 ${\Omega }_{\gamma }$, and obtain several sharp results.

18 pages

References in corpus (1)

• Bohr--Rogosinski radius for analytic functions

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