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