We introduce and study a class of starlike functions associated with a non-convex domain \(\begin{aligned} \mathcal {S}^*_{nc} = \left\{ f \in \mathcal {A}: \frac{z f'(z)}{f(z)} \prec \frac{1+z}{\cos {z}} =: \varphi _{nc}(z), \;\; z \in \mathbb {D} \right\} . \end{aligned}\) Key results include the growth and distortion theorems, initial coefficient bounds, and the sharp estimates for third-order Hankel and Hermitian-Toeplitz determinants. We also examine inclusion relations, radius problems for certain subclasses, and subordination results. These findings enrich the theory of starlike functions associated with a non-convex domains, offering new perspectives in geometric function theory.
