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Two Families of Bi-Univalent Functions Associating the ( p , q )-Derivative with Generalized Bivariate Fibonacci Polynomials

Author

Listed:
  • Sondekola Rudra Swamy

    (Department of Infomation Science and Engineering, Acharya Institute of Technology, Bengaluru 560 107, Karnataka, India
    These authors contributed equally to this work.)

  • Basem Aref Frasin

    (Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq, Jordan
    These authors contributed equally to this work.)

  • Daniel Breaz

    (Department of Computing, Mathematics and Electronics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania
    These authors contributed equally to this work.)

  • Luminita-Ioana Cotîrlă

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

Abstract

Making use of generalized bivariate Fibonacci polynomials, we propose two families of regular functions of the type ϕ ( ζ ) = ζ + ∑ j = 2 ∞ d j ζ j , which are bi-univalent in the disc { ζ ∈ C : | ζ | < 1 } involving the ( p , q )-derivative operator. We find estimates on the coefficients | d 2 | , | d 3 | and the of Fekete–Szegö functional for members of these families. Relevant connections to the existing results and new consequences of the main result are presented.

Suggested Citation

  • Sondekola Rudra Swamy & Basem Aref Frasin & Daniel Breaz & Luminita-Ioana Cotîrlă, 2024. "Two Families of Bi-Univalent Functions Associating the ( p , q )-Derivative with Generalized Bivariate Fibonacci Polynomials," Mathematics, MDPI, vol. 12(24), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:3933-:d:1543551
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