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Subclasses of Bi-Univalent Functions Defined by Frasin Differential Operator

Author

Listed:
  • Ibtisam Aldawish

    (Department of Mathematics and Statistics, College of Science, IMSIU (Imam Mohammed Ibn Saud Islamic University), P.O. Box 90950, Riyadh 11623, Saudi Arabia)

  • Tariq Al-Hawary

    (Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, Jordan)

  • B. A. Frasin

    (Faculty of Science, Department of Mathematics, Al al-Bayt University, Mafraq 25113, Jordan)

Abstract

Let Ω denote the class of functions f ( z ) = z + a 2 z 2 + a 3 z 3 + ⋯ belonging to the normalized analytic function class A in the open unit disk U = z : z < 1 , which are bi-univalent in U , that is, both the function f and its inverse f − 1 are univalent in U . In this paper, we introduce and investigate two new subclasses of the function class Ω of bi-univalent functions defined in the open unit disc U , which are associated with a new differential operator of analytic functions involving binomial series. Furthermore, we find estimates on the Taylor–Maclaurin coefficients | a 2 | and | a 3 | for functions in these new subclasses. Several (known or new) consequences of the results are also pointed out.

Suggested Citation

  • Ibtisam Aldawish & Tariq Al-Hawary & B. A. Frasin, 2020. "Subclasses of Bi-Univalent Functions Defined by Frasin Differential Operator," Mathematics, MDPI, vol. 8(5), pages 1-11, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:783-:d:357376
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    References listed on IDEAS

    as
    1. F. M. Al-Oboudi, 2004. "On univalent functions defined by a generalized Sălăgean operator," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-8, January.
    2. G. Murugusundaramoorthy & N. Magesh & V. Prameela, 2013. "Coefficient Bounds for Certain Subclasses of Bi-Univalent Function," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-3, June.
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    Cited by:

    1. Georgia Irina Oros, 2022. "Geometrical Theory of Analytic Functions," Mathematics, MDPI, vol. 10(18), pages 1-4, September.

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