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Faber Polynomial Coefficient Estimates for Bi-Univalent Functions Defined by Using Differential Subordination and a Certain Fractional Derivative Operator

Author

Listed:
  • Hari M. Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan)

  • Ahmad Motamednezhad

    (Faculty of Mathematical Sciences, Shahrood University of Technology, P. O. Box 36155-316, Shahrood 36155-316, Iran)

  • Ebrahim Analouei Adegani

    (Faculty of Mathematical Sciences, Shahrood University of Technology, P. O. Box 36155-316, Shahrood 36155-316, Iran)

Abstract

In this article, we introduce a general family of analytic and bi-univalent functions in the open unit disk, which is defined by applying the principle of differential subordination between analytic functions and the Tremblay fractional derivative operator. The upper bounds for the general coefficients | a n | of functions in this subclass are found by using the Faber polynomial expansion. We have thereby generalized and improved some of the previously published results.

Suggested Citation

  • Hari M. Srivastava & Ahmad Motamednezhad & Ebrahim Analouei Adegani, 2020. "Faber Polynomial Coefficient Estimates for Bi-Univalent Functions Defined by Using Differential Subordination and a Certain Fractional Derivative Operator," Mathematics, MDPI, vol. 8(2), pages 1-12, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:172-:d:315146
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    Cited by:

    1. Daniel Breaz & Abbas Kareem Wanas & Fethiye Müge Sakar & Seher Melike Aydoǧan, 2023. "On a Fekete–Szegö Problem Associated with Generalized Telephone Numbers," Mathematics, MDPI, vol. 11(15), pages 1-8, July.
    2. Jie Zhai & Rekha Srivastava & Jin-Lin Liu, 2022. "Faber Polynomial Coefficient Estimates of Bi-Close-to-Convex Functions Associated with Generalized Hypergeometric Functions," Mathematics, MDPI, vol. 10(17), pages 1-11, August.

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