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 and Luminita-Ioana Cotîrlă ()
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Mohammad El-Ityan: Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Al-Salt 19117, Jordan
Qasim Ali Shakir: Department of Mathematics, College of Computer Science and Information Technology, University of Al-Qadisiyah, Diwaniyah 58006, Iraq
Tariq Al-Hawary: Department of Applied Science, Ajloun College, Al Balqa Applied University, Ajloun 26816, Jordan
Rafid Buti: Department of Mathematics, College of Education for Pure Science, Al Muthanna University, Al Muthanna 66002, Iraq
Daniel Breaz: Department of Mathematics, University of Alba Iulia, 510009 Alba Iulia, Romania
Luminita-Ioana Cotîrlă: Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania

Mathematics, 2025, vol. 13, issue 8, 1-14

Abstract: 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 | ℓ 5 | . 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 | ℓ 2 | and | ℓ 3 | . 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.

Keywords: ( p , q )-derivative operator; Fekete–Szegö; Hankel determinants; univalent; bi-univalent functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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