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Upper Bound of Second Hankel Determinant for Certain Subclasses of Analytic Functions

Author

Listed:
  • Ming-Sheng Liu
  • Jun-Feng Xu
  • Ming Yang

Abstract

In this present investigation, we first give a survey of the work done so far in this area of Hankel determinant for univalent functions. Then the upper bounds of the second Hankel determinant |a2a4−a32| for functions belonging to the subclasses S(α, β), K(α, β), Ss∗(α,β), and Ks(α, β) of analytic functions are studied. Some of the results, presented in this paper, would extend the corresponding results of earlier authors.

Suggested Citation

  • 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, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:603180
    DOI: 10.1155/2014/603180
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    References listed on IDEAS

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    1. M. Arif & K. I. Noor & M. Raza & W. Haq, 2012. "Some Properties of a Generalized Class of Analytic Functions Related with Janowski Functions," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-11, May.
    2. A. K. Mishra & P. Gochhayat, 2008. "Second Hankel Determinant for a Class of Analytic Functions Defined by Fractional Derivative," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2008, pages 1-10, March.
    3. K. Inayat Noor, 1980. "On the Hankel determinants of close-to-convex univalent functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 3, pages 1-5, January.
    4. Rabha W. Ibrahim, 2013. "Bounded Nonlinear Functional Derived by the Generalized Srivastava-Owa Fractional Differential Operator," International Journal of Analysis, Hindawi, vol. 2013, pages 1-7, January.
    5. Sarika Verma & Sushma Gupta & Sukhjit Singh, 2012. "Bounds of Hankel Determinant for a Class of Univalent Functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-6, July.
    6. M. Arif & K. I. Noor & M. Raza & W. Haq, 2012. "Some Properties of a Generalized Class of Analytic Functions Related with Janowski Functions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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    Cited by:

    1. Mohammad Faisal Khan & Mohammed Abaoud & Naeem Ahmad & Muqrin A Almuqrin, 2025. "New class of symmetric starlike functions subordinate to the generating function of Gregory coefficients," PLOS ONE, Public Library of Science, vol. 20(5), pages 1-20, May.
    2. Paweł Zaprawa, 2016. "Second Hankel Determinants for the Class of Typically Real Functions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2016(1).
    3. Farah Zulfiqar & Sarfraz Nawaz Malik & Mohsan Raza & Md. Shajib Ali, 2022. "Fourth‐Order Hankel Determinants and Toeplitz Determinants for Convex Functions Connected with Sine Functions," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).

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