Starlike Functions Associated with a Non-Convex Domain

We introduce and study a class of starlike functions associated with the non-convex domain $${\mathcal{S}}_{nc}^{\ast }=\{f\in \mathcal{A}:\frac{z{f}^{\mathrm{\prime }}(z)}{f(z)}\prec \frac{1+z}{\cos z}=:{\phi }_{nc}(z),z\in \mathbb{D}\}\mathrm{.}$$ 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 non-convex domains, offering new perspectives in geometric function theory.