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Third-Order Hankel Determinant for a Class of Bi-Univalent Functions Associated with Sine Function

Author

Listed:
  • Mohammad El-Ityan

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

  • Mustafa A. Sabri

    (Department of Mathematics, College of Education, Mustansiriyah University, Baghdad 10052, Iraq
    These authors contributed equally to this work.)

  • Suha Hammad

    (Department of Mathematics, College of Education for Pure Sciences, University of Tikrit, Tikrit 34001, Iraq
    These authors contributed equally to this work.)

  • Basem Frasin

    (Department of Mathematics, Faculty of Science, Al Al-Bayt University, Mafraq 25113, Jordan
    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.)

  • Feras Yousef

    (Department of Mathematics, The University of Jordan, Amman 11942, Jordan
    These authors contributed equally to this work.)

Abstract

This paper investigates a new subclass of bi-univalent analytic functions defined on the open unit disk in the complex plane, associated with the subordination to 1 + s i n z . Coefficient bounds are obtained for the initial Taylor–Maclaurin coefficients, with a particular focus on the second- and third-order Hankel determinants. To illustrate the non-emptiness of the proposed class, we consider the function 1 + tanh z , which maps the unit disk onto a bean-shaped domain. This function satisfies the required subordination condition and hence serves as an explicit member of the class. A graphical depiction of the image domain is provided to highlight its geometric characteristics. The results obtained in this work confirm that the class under study is non-trivial and possesses rich geometric structure, making it suitable for further development in the theory of geometric function classes and coefficient estimation problems.

Suggested Citation

  • Mohammad El-Ityan & Mustafa A. Sabri & Suha Hammad & Basem Frasin & Tariq Al-Hawary & Feras Yousef, 2025. "Third-Order Hankel Determinant for a Class of Bi-Univalent Functions Associated with Sine Function," Mathematics, MDPI, vol. 13(17), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:17:p:2887-:d:1743804
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