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Investigation of the Hankel Determinant Sharp Bounds for a Specific Analytic Function Linked to a Cardioid-Shaped Domain

Author

Listed:
  • Isra Al-Shbeil

    (Department of Mathematics, Faculty of Science, The University of Jordon, Amman 11942, Jordan)

  • Muhammad Imran Faisal

    (Department of Mathematics, Taibah University, Universities Road, P.O. Box 344, Medina 42317, Saudi Arabia)

  • Muhammad Arif

    (Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan)

  • Muhammad Abbas

    (Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan)

  • Reem K. Alhefthi

    (Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

Abstract

One of the challenging tasks in the study of function theory is how to obtain sharp estimates of coefficients that appear in the Taylor–Maclaurin series of analytic univalent functions, and for obtaining these bounds, researchers used the concepts of Carathéodory functions. Among these coefficient-related problems, the problem of the third-order Hankel determinant sharp bound is the most difficult one. The aim of the present study is to determine the sharp bound of the Hankel determinant of third order by using the methodology of the aforementioned Carathéodory function family. Further, we also study some other coefficient-related problems, such as the Fekete–Szegő inequality and the second-order Hankel determinant. We examine these results for the family of bounded turning functions linked with a cardioid-shaped domain.

Suggested Citation

  • Isra Al-Shbeil & Muhammad Imran Faisal & Muhammad Arif & Muhammad Abbas & Reem K. Alhefthi, 2023. "Investigation of the Hankel Determinant Sharp Bounds for a Specific Analytic Function Linked to a Cardioid-Shaped Domain," Mathematics, MDPI, vol. 11(17), pages 1-22, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3664-:d:1224704
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    References listed on IDEAS

    as
    1. Oh Sang Kwon & Young Jae Sim, 2019. "The Sharp Bound of the Hankel Determinant of the Third Kind for Starlike Functions with Real Coefficients," Mathematics, MDPI, vol. 7(8), pages 1-14, August.
    2. Lei Shi & Izaz Ali & Muhammad Arif & Nak Eun Cho & Shehzad Hussain & Hassan Khan, 2019. "A Study of Third Hankel Determinant Problem for Certain Subfamilies of Analytic Functions Involving Cardioid Domain," Mathematics, MDPI, vol. 7(5), pages 1-15, May.
    3. Lei Shi & Muhammad Arif & Mohsan Raza & Muhammad Abbas, 2022. "Hankel Determinant Containing Logarithmic Coefficients for Bounded Turning Functions Connected to a Three-Leaf-Shaped Domain," Mathematics, MDPI, vol. 10(16), pages 1-10, August.
    4. Abdullah Alotaibi & Muhammad Arif & Mohammed A. Alghamdi & Shehzad Hussain, 2020. "Starlikness Associated with Cosine Hyperbolic Function," Mathematics, MDPI, vol. 8(7), pages 1-16, July.
    5. Hari M. Srivastava & Qazi Zahoor Ahmad & Nasir Khan & Nazar Khan & Bilal Khan, 2019. "Hankel and Toeplitz Determinants for a Subclass of q -Starlike Functions Associated with a General Conic Domain," Mathematics, MDPI, vol. 7(2), pages 1-15, February.
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