  Let $ \mathcal{H}(\mathbb{D}) $ be the class of analytic functions in the
unit disk $ \mathbb{D} : =\{z\in\mathbb{C} : |z|<1\} $. The classical Bohr's
inequality states that if a power series $ f(z)=\sum_{n=0}^{\infty}a_nz^n $
converges in $ \mathbb{D} $ and $ |f(z)|<1 $ for $ z\in\mathbb{D} $, then
  \begin{equation*}
  \sum_{n=0}^{\infty}|a_n|r^n\leq 1\;\;\mbox{for}\;\; r\leq \frac{1}{3}
  \end{equation*} and the constant $ 1/3 $ cannot be improved. The constant $
1/3 $ is known as Bohr radius. In this paper, we study Bohr phenomenon for
analytic as well as harmonic mappings on simply connected domains. We prove
several sharp results on improved Bohr radius for analytic functions as well as
for harmonic mappings on simply connected domains.
