We introduce and study a class of starlike functions associated with the non-convex domain \[ \mathcal{ S}^*_{ nc} = \left\{ f \in \mathcal{ A} : \frac{ z f'(z)}{ f(z)} \prec \frac{ 1+z}{ \cos{ z}} =: \varphi_{ nc}(z), \;\; z \in \mathbb{ D} \right\}. \] 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.
Categories: math.CV