Hankel determinant and Toeplitz determinant for the class of Convex functions associated with an epicycloid

In this paper, we investigate the class of convex functions associated with an epicycloid, denoted by 𝒞 nL . We derive sharp bounds for several important functionals, including the Fekete-Szegö functional, initial coefficient differences, Hankel determinants, and symmetric Toeplitz determinants of various orders for functions belonging to this class. In addition, we establish corresponding sharp coefficient bounds for the inverse functions. Our approach utilizes subordination principles and extremal properties of Carathéodory functions to obtain the main results. These findings contribute to the broader understanding of geometric function theory by extending coefficient and determinant inequalities to a recently introduced family of convex functions.