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Hankel Determinant Containing Logarithmic Coefficients for Bounded Turning Functions Connected to a Three-Leaf-Shaped Domain

Author

Listed:
  • Lei Shi

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

  • Muhammad Arif

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

  • Mohsan Raza

    (Department of Mathematics, Government College University, Faisalabad 38000, Pakistan)

  • Muhammad Abbas

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

Abstract

The purpose of this study was to obtain the sharp Hankel determinant H 2 , 1 F f / 2 and H 2 , 2 F f / 2 with a logarithmic coefficient as entry for the class BT 3 L of bounded turning functions connected with a three-leaf-shaped domain. In this study, we developed a novel method to prove the bound sharpness. Although the calculations are much easier using numerical analysis, all the proofs of our results can be checked with a basic knowledge of calculus.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2924-:d:887821
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    References listed on IDEAS

    as
    1. 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.
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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.
    2. 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.
    3. 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.

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    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.

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