On the Third Hankel Determinant of a Certain Subclass of Bi-Univalent Functions Defined by (p,q)-Derivative Operator

In this study, the generalized (p,q)-derivative operator is used to define a novel class of bi-univalent functions. For this class, we define constraints on the coefficients up to |ℓ5|. The functions are analyzed using a suitable operational method, which enables us to derive new bounds for the Fekete–Szegö functional, as well as explicit estimates for important coefficients like |ℓ2| and |ℓ3|. In addition, we establish the upper bounds of the second and third Hankel determinants, providing insights into the geometrical and analytical properties of this class of functions.