A class of close-to-star functions CSφ = {f ∈ A : (1−z) 2 f(z)/z ≺ φ(z)} defined by subordination is presented in this study. For the class CSφ , coefficient estimates, bounds for the second and third order Hermitian Toeplitz determinants, and Fekete-Szegö inequality is established. Further, Hermitian Toeplitz determinants and Fekete-Szegö inequality are discussed for specific cases of φ.

This study of Hankel and Hermitian Toeplitz determinants is one of the major areas of interest in Geometric function theory and has wide applications in the areas of signal processing and Applied Mathematics. In our present investigations, we define a new subclass of normalized analytic functions $\mathfrak{H}\left(\lambda \right)$$(\lambda \ge 0)$, defined using a subordination relation with the sine function $\mathcal{K}\left(z\right)=1+sinz$. For the class $\mathfrak{H}\left(\lambda \right)$, coefficient estimates, upper and lower bounds for the Hermitian Toeplitz determinants of second and third order are found. In addition, estimates are provided for the second and third-order Hankel determinants for the class $\mathfrak{H}\left(\lambda \right)$.