On a Subclass of Starlike Functions Associated with a Strip Domain

Abstract

In the present investigation, we introduce a new subclass of starlike functions defined by ${\mathcal{S}}_{\tau }^{\ast }:=\{f\in \mathcal{A}:z{f}^{\prime }(z)/f(z)\prec 1+\arctan z=:\tau (z)\}$, where $\tau (z)$ maps the unit disk $\mathbb{D}:=\{z\in \mathbb{C}:|z|<1\}$ onto a strip domain. We derive structural formulae, growth, and distortion theorems for ${\mathcal{S}}_{\tau }^{\ast }$. Also, inclusion relations with some well-known subclasses of $\mathcal{S}$ are established and obtain sharp radius estimates, as well as sharp coefficient bounds for the initial five coefficients and the second and third-order Hankel determinants of ${\mathcal{S}}_{\tau }^{\ast }$.