A generalization of the Bohr inequality for bounded analytic functions on simply connected domains and its applications

Abstract

Bohr's classical theorem and its generalizations are now active areas of research and have been the source of investigations in numerous function spaces. In this article, we study a generalized Bohr's inequality for the class of bounded analytic functions defined on the simply connected domain $${\Omega }_{\gamma }:=\{z\in \mathbb{C}:|z+\frac{\gamma }{1-\gamma }|<\frac{1}{1-\gamma }\},\text{for }0\le \gamma <1.$$ Part of its applications, we calculate the Bohr-type radii for some known integral operators.

References in corpus (6)

• On the Bohr inequality
• The Bohr Phenomenon for analytic functions on simply connected domains
• Bohr phenomenon for locally univalent functions and logarithmic power series
• Bohr operator on analytic functions
• Generalization of Bohr-type inequality in analytic functions
• Bohr type inequality for {C}esáro and {B}ernardi integral operator on simply connected domain

Cited by in corpus (1)

• Generalized Bohr inequalities for K-quasiconformal harmonic mappings and their applications