Let \( {\mathcal {H}} \) be the class of harmonic functions \( f=h+{\bar{g}} \) in the unit disk \({\mathbb {D}}:=\{z\in {\mathbb {C}} : |z|<1\}\), where h and g are analytic in \( {\mathbb {D}} \). Let \({\mathcal {P}}_{{\mathcal {H}}}^{0}(\alpha )=\{f=h+{\overline{g}} \in {\mathcal {H}} : {{\text {Re}}\,}(h^{\prime }(z)-\alpha )>|g^{\prime }(z)|\; \text{ with }\; 0\le \alpha <1,\; g^{\prime }(0)=0,\; z \in {\mathbb {D}}\} \) be the class of close-to-convex mappings defined by Li and Ponnusamy (Nonlinear Anal 89:276–283, 2013). In this paper, we obtain the sharp Bohr–Rogosinski radius, improved Bohr radius and refined Bohr radius for the class \( {\mathcal {P}}_{{\mathcal {H}}}^{0}(\alpha ) \).

让\（{\ mathcal {H}} \）是类的调和函数\（F = H + {\酒吧{G}} \）在单位圆盘\（{\ mathbb {d}}：= \ {Z \ in {\ mathbb {C}}：| z | <1 \} \），其中h和g在\（{\ mathbb {D}} \）中进行解析。让\（{\ mathcal {P}} _ {{\ mathcal {H}}} ^ {0}（\ alpha）= \ {f = h + {\ overline {g}} \ in {\ mathcal {H}} ：{{\ text {Re}} \，}（h ^ {\ prime}（z）-\ alpha）> | g ^ {\ prime}（z）| \; \ text {和} \; 0 \ le \ alpha <1，\; g ^ {\ prime}（0）= 0，\; {\ mathbb {D}} \} \）中的z \是Li和Ponnusamy定义的近凸映射的一类（非线性肛门89：276-283，2013年）。在本文中，我们获得了该类的尖锐的玻尔-罗戈辛斯基半径，改进的玻尔半径和精制的玻尔半径\（{\ mathcal {P}} _ {{\ mathcal {H}}} ^ {0}（\ alpha} \）。