On the Third Hankel Determinant of a Certain Subclass of Bi-Univalent Functions Defined by (p,q)-Derivative Operator - Mohammad El-Ityan; Qasim Ali Shakir; Tariq Al-Hawary; Rafid Buti; Daniel Breaz; Luminita-Ioana Cotîrlă (Mathematics)
In this study, the generalized <semantics>(p,q)</semantics>-derivative operator is used to define a novel class of bi-univalent functions. For this class, we define constraints on the coefficients up to <semantics>|ℓ5|</semantics>. 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 <semantics>|ℓ2|</semantics> and <semantics>|ℓ3|</semantics>. 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.