Improved Bohr inequalities for certain class of harmonic univalent functions

Let $\mathcal{H}$ be the class of complex-valued harmonic mappings $f=h+\bar{g}$ defined in the unit disk $\mathbb{D} : =\{z\in\mathbb{C} : |z|<1\}$, 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 $\mathcal{H}_{0}=\{f=h+\bar{g}\in\mathcal{H} : g^{\prime}(0)=0\}.$ Ghosh and Vasudevrao \cite{Ghosh-Vasudevarao-BAMS-2020} have studied the following interesting harmonic univalent class $\mathcal{P}^{0}_{\mathcal{H}}(M)$ which is defined by $$\mathcal{P}^{0}_{\mathcal{H}}(M) :=\{f=h+\overline{g} \in \mathcal{H}_{0}: \mathrm{Re} (zh^{\prime\prime}(z))> -M+|zg^{\prime\prime}(z)|,\; z \in \mathbb{D}\; \mbox{and}\;\; M>0\}.$$ In this paper, we obtain the sharp Bohr-Rogosinski inequality, improved Bohr inequality, refined Bohr inequality and Bohr-type inequality for the class $\mathcal{P}_{\mathcal{H}}^{0}(M)$.