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Some Further Coefficient Bounds on a New Subclass of Analytic Functions

Author

Listed:
  • Yue-Juan Sun

    (School of Mathematics and Statistics, Shangqiu Normal University, Shangqiu 476000, China)

  • Muhammad Arif

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

  • Lei Shi

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

  • Muhammad Imran Faisal

    (Mathematics Department, Taibah University, Universities Road, P.O. Box 344, Medina 42353, Saudi Arabia)

Abstract

The coefficient problem is an essential topic in the theory of univalent functions theory. In the present paper, we consider a new subclass SQ of analytic functions with f ′ ( z ) subordinated to 1 / ( 1 − z ) 2 in the open unit disk. This class was introduced and studied by Răducanu. Our main aim is to give the sharp upper bounds of the second Hankel determinant H 2 , 3 f and the third Hankel determinant H 3 , 1 f for f ∈ SQ . This may help to understand more properties of functions in this class and inspire further investigations on higher Hankel determinants for this or other popular sub-classes of univalent functions.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2784-:d:1175540
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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 & 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.
    3. Gangadharan Murugusundaramoorthy & Teodor Bulboacă, 2020. "Hankel Determinants for New Subclasses of Analytic Functions Related to a Shell Shaped Region," Mathematics, MDPI, vol. 8(6), pages 1-14, June.
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