Bohr radius for certain close-to-convex harmonic mappings

Abstract

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 $$\mathcal{P}_{\mathcal{H}}^{0}(α)=\{f=h+\overline{g} \in \mathcal{H} : \real (h^{\prime}(z)-α)>|g^{\prime}(z)|\; \mbox{with}\; 0\leqα<1,\; g^{\prime}(0)=0,\; z \in \mathbb{D}\} $$ be the class of close-to-convex mappings defined by Li and Ponnusamy \cite{Injectivity section}. In this paper, we obtain the sharp Bohr-Rogosinski radius, improved Bohr radius and refined Bohr radius for the class ${\mathcal{P}}_{\mathcal{H}}^0(\alpha )$.

26 pages, 21 figures

References in corpus (1)

• Refined Bohr inequality for bounded analytic functions