  The classical Bohr inequality states that if $ f $ is an analytic function
with the power series representation $ f(z)=\sum_{n=0}^{\infty}a_nz^n $ in the
unit disk $ \mathbb{D}:=\{z\in\mathbb{C} : |z|<1\} $ such that $ |f(z)|\leq 1 $
for all $ z\in\mathbb{D} $, then \begin{equation*}
  \sum_{n=0}^{\infty}|a_n|r^n\leq 1\;\; \text{for}\;\; |z|=r\leq\frac{1}{3}
\end{equation*} and the constant $ 1/3 $ cannot be improved. The constant $
r_0=1/3 $ is known as Bohr radius and the inequality $
\sum_{n=0}^{\infty}|a_n|r^n\leq 1 $ is known as Bohr inequality. Let $
\mathcal{H} $ be the class of complex-valued harmonic mappings $ f=h+\bar{g}$
defined in the unit disk $ \mathbb{D} $, where $ h $ and $ g $ are analytic
functions in $ \mathbb{D} $ with the normalization $ h(0)=0=h^{\prime}(0)-1 $
and $ g(0)=0 $. Let $ \mathcal{H}_{0}=\{f=h+\bar{g}\in\mathcal{H} :
g^{\prime}(0)=0\}. $ Let $ \mathcal{P}^{0}_{\mathcal{H}}(M)
:=\{f=h+\overline{g} \in \mathcal{H}_{0}: \real (zh^{\prime\prime}(z))>
-M+|zg^{\prime\prime}(z)|,\; z \in \mathbb{D},\; M>0\} $. Functions in the
class $ \mathcal{P}^{0}_{\mathcal{H}}(M) $ are called fully starlike univalent
functions for $ 0<M<1/\log 4 $. In this paper, we obtain the sharp
Bohr-Rogosinski type inequality and improved Bohr inequality and the
corresponding Bohr radius for the class $ \mathcal{P}_{\mathcal{H}}^{0}(M) $.
