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A Study of Third Hankel Determinant Problem for Certain Subfamilies of Analytic Functions Involving Cardioid Domain

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  • Lei Shi

    (School of Mathematics and Statistics, Anyang Normal University, Anyang 455002, China)

  • Izaz Ali

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

  • Muhammad Arif

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

  • Nak Eun Cho

    (Department of Applied Mathematics, Pukyong National University, Busan 48513, Korea)

  • Shehzad Hussain

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

  • Hassan Khan

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

Abstract

In the present article, we consider certain subfamilies of analytic functions connected with the cardioid domain in the region of the unit disk. The purpose of this article is to investigate the estimates of the third Hankel determinant for these families. Further, the same bounds have been investigated for two-fold and three-fold symmetric functions.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:418-:d:230023
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    References listed on IDEAS

    as
    1. Ming-Sheng Liu & Jun-Feng Xu & Ming Yang, 2014. "Upper Bound of Second Hankel Determinant for Certain Subclasses of Analytic Functions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, June.
    2. T. N. Shanmugam, 1989. "Convolution and differential subordination," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 12, pages 1-8, January.
    3. 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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    Cited by:

    1. 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.

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