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

Author

Listed:
  • Mohammad El-Ityan

    (Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Al-Salt 19117, Jordan
    These authors contributed equally to this work.)

  • Qasim Ali Shakir

    (Department of Mathematics, College of Computer Science and Information Technology, University of Al-Qadisiyah, Diwaniyah 58006, Iraq
    These authors contributed equally to this work.)

  • Tariq Al-Hawary

    (Department of Applied Science, Ajloun College, Al Balqa Applied University, Ajloun 26816, Jordan
    These authors contributed equally to this work.)

  • Rafid Buti

    (Department of Mathematics, College of Education for Pure Science, Al Muthanna University, Al Muthanna 66002, Iraq
    These authors contributed equally to this work.)

  • Daniel Breaz

    (Department of Mathematics, University of Alba Iulia, 510009 Alba Iulia, Romania
    These authors contributed equally to this work.)

  • Luminita-Ioana Cotîrlă

    (Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Mohammad El-Ityan & Qasim Ali Shakir & Tariq Al-Hawary & Rafid Buti & Daniel Breaz & Luminita-Ioana Cotîrlă, 2025. "On the Third Hankel Determinant of a Certain Subclass of Bi-Univalent Functions Defined by ( p , q )-Derivative Operator," Mathematics, MDPI, vol. 13(8), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:8:p:1269-:d:1633223
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