A generalization of the Bohr inequality and its applications

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