Bohr radius for certain classes of close-to-convex harmonic mappings

Let H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathcal {H}} $$\end{document} be the class of harmonic functions f=h+g¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ f=h+{\bar{g}} $$\end{document} in the unit disk D:={z∈C:|z|<1}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {D}}:=\{z\in {\mathbb {C}} : |z|<1\}$$\end{document}, where h and g are analytic in D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathbb {D}} $$\end{document}. Let PH0(α)={f=h+g¯∈H:Re(h′(z)-α)>|g′(z)|with0≤α<1,g′(0)=0,z∈D}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {P}}_{{\mathcal {H}}}^{0}(\alpha )=\{f=h+{\overline{g}} \in {\mathcal {H}} : {{\text {Re}}\,}(h^{\prime }(z)-\alpha )>|g^{\prime }(z)|\; \text{ with }\; 0\le \alpha <1,\; g^{\prime }(0)=0,\; z \in {\mathbb {D}}\} $$\end{document} 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 PH0(α)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathcal {P}}_{{\mathcal {H}}}^{0}(\alpha ) $$\end{document}.