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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} $ withthe 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 andVasudevrao \cite{Ghosh-Vasudevarao-BAMS-2020} have studied the followinginteresting harmonic univalent class $ \mathcal{P}^{0}_{\mathcal{H}}(M) $ whichis 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, improvedBohr inequality, refined Bohr inequality and Bohr-type inequality for the class$ \mathcal{P}_{\mathcal{H}}^{0}(M) $.

Improved Bohr inequalities for certain class of harmonic univalent functions