Our study aims to introduce a new subclass of star-like functions characterized by symmetric points subordinated to a strip domain. In particular, the class is defined as follows: \(\mathcal {SSP}_{\tau }^{*}= \bigg \{f \in \mathcal {A}: \frac{2zf^{\prime }(z)}{f(z)-f(-z)} \prec \tau (z)\bigg \}\) , where \(\mathcal {A}\) represents the family of analytic normalized functions. We investigate various analytic characteristics of this function that belongs to the class, including the coefficient bounds and determinants. We have derived bounds for the Fekete–Szego inequality and examined second- and third-order Hankel determinants, Toeplitz determinants, and Vandermonde determinants, respectively. These results contribute to a deeper understanding of geometric function theory, especially in the context of functions with symmetric properties in the class.
