IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i17p3664-d1224704.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/17/3664/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/17/3664/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Muhammad Arif & Safa Marwa & Qin Xin & Fairouz Tchier & Muhammad Ayaz & Sarfraz Nawaz Malik, 2022. "Sharp Coefficient Problems of Functions with Bounded Turnings Subordinated by Sigmoid Function," Mathematics, MDPI, vol. 10(20), pages 1-24, October.
    2. Lei Shi & Muhammad Arif & Ayesha Rafiq & Muhammad Abbas & Javed Iqbal, 2022. "Sharp Bounds of Hankel Determinant on Logarithmic Coefficients for Functions of Bounded Turning Associated with Petal-Shaped Domain," Mathematics, MDPI, vol. 10(11), pages 1-19, June.
    3. Mohsan Raza & Hari Mohan Srivastava & Qin Xin & Fairouz Tchier & Sarfraz Nawaz Malik & Muhammad Arif, 2023. "Starlikeness Associated with the Van Der Pol Numbers," Mathematics, MDPI, vol. 11(10), pages 1-22, May.
    4. Rabha W. Ibrahim & Rafida M. Elobaid & Suzan J. Obaiys, 2020. "A Class of Quantum Briot–Bouquet Differential Equations with Complex Coefficients," Mathematics, MDPI, vol. 8(5), pages 1-13, May.
    5. Huo Tang & Ihtesham Gul & Saqib Hussain & Saima Noor, 2023. "Bounds for Toeplitz Determinants and Related Inequalities for a New Subclass of Analytic Functions," Mathematics, MDPI, vol. 11(18), pages 1-15, September.
    6. Hai-Yan Zhang & Rekha Srivastava & Huo Tang, 2019. "Third-Order Hankel and Toeplitz Determinants for Starlike Functions Connected with the Sine Function," Mathematics, MDPI, vol. 7(5), pages 1-10, May.
    7. Shahid Khan & Saqib Hussain & Muhammad Naeem & Maslina Darus & Akhter Rasheed, 2021. "A Subclass of q -Starlike Functions Defined by Using a Symmetric q -Derivative Operator and Related with Generalized Symmetric Conic Domains," Mathematics, MDPI, vol. 9(9), pages 1-12, April.
    8. Miraj Ul-Haq & Mohsan Raza & Muhammad Arif & Qaiser Khan & Huo Tang, 2019. "q-Analogue of Differential Subordinations," Mathematics, MDPI, vol. 7(8), pages 1-16, August.
    9. Saeed Islam & Muhammad Ghaffar Khan & Bakhtiar Ahmad & Muhammad Arif & Ronnason Chinram, 2020. "Q -Extension of Starlike Functions Subordinated with a Trigonometric Sine Function," Mathematics, MDPI, vol. 8(10), pages 1-14, October.
    10. Hari M. Srivastava & Nazar Khan & Shahid Khan & Qazi Zahoor Ahmad & Bilal Khan, 2021. "A Class of k -Symmetric Harmonic Functions Involving a Certain q -Derivative Operator," Mathematics, MDPI, vol. 9(15), pages 1-14, July.
    11. Georgia Irina Oros, 2022. "Geometrical Theory of Analytic Functions," Mathematics, MDPI, vol. 10(18), pages 1-4, September.
    12. Hari Mohan Srivastava & Nazar Khan & Maslina Darus & Shahid Khan & Qazi Zahoor Ahmad & Saqib Hussain, 2020. "Fekete-Szegö Type Problems and Their Applications for a Subclass of q -Starlike Functions with Respect to Symmetrical Points," Mathematics, MDPI, vol. 8(5), pages 1-18, May.
    13. Yue-Juan Sun & Muhammad Arif & Lei Shi & Muhammad Imran Faisal, 2023. "Some Further Coefficient Bounds on a New Subclass of Analytic Functions," Mathematics, MDPI, vol. 11(12), pages 1-14, June.
    14. Nazar Khan & Shahid Khan & Qin Xin & Fairouz Tchier & Sarfraz Nawaz Malik & Umer Javed, 2023. "Some Applications of Analytic Functions Associated with q -Fractional Operator," Mathematics, MDPI, vol. 11(4), pages 1-17, February.
    15. Lei Shi & Hari M. Srivastava & Ayesha Rafiq & Muhammad Arif & Muhammad Ihsan, 2022. "Results on Hankel Determinants for the Inverse of Certain Analytic Functions Subordinated to the Exponential Function," Mathematics, MDPI, vol. 10(19), pages 1-15, September.
    16. Qaiser Khan & Muhammad Arif & Mohsan Raza & Gautam Srivastava & Huo Tang & Shafiq ur Rehman, 2019. "Some Applications of a New Integral Operator in q -Analog for Multivalent Functions," Mathematics, MDPI, vol. 7(12), pages 1-13, December.
    17. Dong Guo & Huo Tang & Zongtao Li & Qingbing Xu & En Ao, 2023. "Coefficient Problems for a Class of Univalent Functions," Mathematics, MDPI, vol. 11(8), pages 1-14, April.
    18. 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.
    19. Lei Shi & Qaiser Khan & Gautam Srivastava & Jin-Lin Liu & Muhammad Arif, 2019. "A Study of Multivalent q -starlike Functions Connected with Circular Domain," Mathematics, MDPI, vol. 7(8), pages 1-12, July.
    20. Isra Al-Shbeil & Afis Saliu & Adriana Cătaş & Sarfraz Nawaz Malik & Semiu Oladipupo Oladejo, 2022. "Some Geometrical Results Associated with Secant Hyperbolic Functions," Mathematics, MDPI, vol. 10(15), pages 1-13, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3664-:d:1224704. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.