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 $\mathcal{S}^{*}_{\tau}:={f\in \mathcal{A}:zf'(z)/f(z) \prec 1+\arctan z=:\tau(z)}$, 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 $\mathcal{S}^{*}_{\tau}$. 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 $\mathcal{S}^{*}_{\tau}$.