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Coefficient Estimates and the Fekete–Szegö Problem for New Classes of m -Fold Symmetric Bi-Univalent Functions

Author

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  • Georgia Irina Oros

    (Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania
    These authors contributed equally to this work.)

  • Luminiţa-Ioana Cotîrlă

    (Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
    These authors contributed equally to this work.)

Abstract

The results presented in this paper deal with the classical but still prevalent problem of introducing new classes of m-fold symmetric bi-univalent functions and studying properties related to coefficient estimates. Quantum calculus aspects are also considered in this study in order to enhance its novelty and to obtain more interesting results. We present three new classes of bi-univalent functions, generalizing certain previously studied classes. The relation between the known results and the new ones presented here is highlighted. Estimates on the Taylor–Maclaurin coefficients | a m + 1 | and | a 2 m + 1 | are obtained and, furthermore, the much investigated aspect of Fekete–Szegő functional is also considered for each of the new classes.

Suggested Citation

  • Georgia Irina Oros & Luminiţa-Ioana Cotîrlă, 2022. "Coefficient Estimates and the Fekete–Szegö Problem for New Classes of m -Fold Symmetric Bi-Univalent Functions," Mathematics, MDPI, vol. 10(1), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:1:p:129-:d:716282
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    Citations

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    Cited by:

    1. Sondekola Rudra Swamy & Basem Aref Frasin & Ibtisam Aldawish, 2022. "Fekete–Szegö Functional Problem for a Special Family of m -Fold Symmetric Bi-Univalent Functions," Mathematics, MDPI, vol. 10(7), pages 1-14, April.
    2. Abdulmtalb Hussen & Abdelbaset Zeyani, 2023. "Coefficients and Fekete–Szegö Functional Estimations of Bi-Univalent Subclasses Based on Gegenbauer Polynomials," Mathematics, MDPI, vol. 11(13), pages 1-10, June.
    3. Abbas Kareem Wanas & Luminiţa-Ioana Cotîrlǎ, 2022. "New Applications of Gegenbauer Polynomials on a New Family of Bi-Bazilevič Functions Governed by the q -Srivastava-Attiya Operator," Mathematics, MDPI, vol. 10(8), pages 1-9, April.
    4. Ridong Wang & Manoj Singh & Shahid Khan & Huo Tang & Mohammad Faisal Khan & Mustafa Kamal, 2023. "New Applications of Faber Polynomial Expansion for Analytical Bi-Close-to-Convex Functions Defined by Using q -Calculus," Mathematics, MDPI, vol. 11(5), pages 1-15, March.

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