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Third-Order Hankel and Toeplitz Determinants for Starlike Functions Connected with the Sine Function

Author

Listed:
  • Hai-Yan Zhang

    (School of Mathematics and Statistics, Chifeng University, Chifeng 024000, China)

  • Rekha Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada)

  • Huo Tang

    (School of Mathematics and Statistics, Chifeng University, Chifeng 024000, China)

Abstract

Let S s * be the class of normalized functions f defined in the open unit disk D = { z : | z | < 1 } such that the quantity z f ′ ( z ) f ( z ) lies in an eight-shaped region in the right-half plane and satisfying the condition z f ′ ( z ) f ( z ) ≺ 1 + sin z ( z ∈ D ) . In this paper, we aim to investigate the third-order Hankel determinant H 3 ( 1 ) and Toeplitz determinant T 3 ( 2 ) for this function class S s * associated with sine function and obtain the upper bounds of the determinants H 3 ( 1 ) and T 3 ( 2 ) .

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:404-:d:228693
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    References listed on IDEAS

    as
    1. 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. Muhammad Naeem & Saqib Hussain & Shahid Khan & Tahir Mahmood & Maslina Darus & Zahid Shareef, 2020. "Janowski Type q -Convex and q -Close-to-Convex Functions Associated with q -Conic Domain," Mathematics, MDPI, vol. 8(3), pages 1-13, March.

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