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Coefficients and Fekete–Szegö Functional Estimations of Bi-Univalent Subclasses Based on Gegenbauer Polynomials

Author

Listed:
  • Abdulmtalb Hussen

    (School of Engineering, Math, and Technology, Navajo Technical University, Lowerpoint Rd State Hwy 371, Crownpoint, NM 87313, USA)

  • Abdelbaset Zeyani

    (Department of Mathematics and Statistics, Wichita State University, Wichita, KS 67260, USA)

Abstract

Subclasses of analytic and bi-univalent functions have been extensively improved and utilized for estimating the Taylor–Maclaurin coefficients and the Fekete–Szegö functional. In this paper, we consider a certain subclass of normalized analytic and bi-univalent functions. These functions have inverses that possess a bi-univalent analytic continuation to an open unit disk and are associated with orthogonal polynomials; namely, Gegenbauer polynomials that satisfy subordination conditions on the open unit disk. We use this subclass to derive new approximations for the second and third Taylor–Maclaurin coefficients and the Fekete–Szegö functional. Furthermore, we discuss several new results that arise when we specialize the parameters used in our fundamental findings.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2852-:d:1179138
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    References listed on IDEAS

    as
    1. Z. Peng & G. Murugusundaramoorthy & T. Janani, 2014. "Coefficient Estimate of Biunivalent Functions of Complex Order Associated with the Hohlov Operator," Journal of Complex Analysis, Hindawi, vol. 2014, pages 1-6, April.
    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.
    3. Ala Amourah & Basem Aref Frasin & Tamer M. Seoudy, 2022. "An Application of Miller–Ross-Type Poisson Distribution on Certain Subclasses of Bi-Univalent Functions Subordinate to Gegenbauer Polynomials," Mathematics, MDPI, vol. 10(14), pages 1-10, July.
    4. 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.
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