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 $areanalyticfunctionsin$ $\mathbb{D}$ $ with the normalization $h(0)=0=h^{\mathrm{\prime }}(0)-1$ and $g(0)=0$. Let ${\mathcal{H}}_0=\{f=h+\bar{g}\in \mathcal{H}:g^{\mathrm{\prime }}(0)=0\}\mathrm{.}$ Ghosh and Vasudevrao \cite{Ghosh-Vasudevarao-BAMS-2020} have studied the following interesting harmonic univalent class ${\mathcal{P}}_{\mathcal{H}}^0(M)$ which is defined by $${\mathcal{P}}_{\mathcal{H}}^0(M):=\{f=h+\bar{g}\in {\mathcal{H}}_0:\mathrm{R}\mathrm{e}(z{h}^{\mathrm{\prime }\mathrm{\prime }}(z))>-M+\mathrm{\mid }z{g}^{\mathrm{\prime }\mathrm{\prime }}(z)\mathrm{\mid },z\in \mathbb{D}andM>0\}\mathrm{.}$$ In this paper, we obtain the sharp Bohr-Rogosinski inequality, improved Bohr inequality, refined Bohr inequality and Bohr-type inequality for the class ${\mathcal{P}}_{\mathcal{H}}^0(M)$.