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

Sondekola Rudra Swamy, Basem Aref Frasin, Daniel Breaz () and Luminita-Ioana Cotîrlă ()
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Sondekola Rudra Swamy: Department of Infomation Science and Engineering, Acharya Institute of Technology, Bengaluru 560 107, Karnataka, India
Basem Aref Frasin: Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq, Jordan
Daniel Breaz: Department of Computing, Mathematics and Electronics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania
Luminita-Ioana Cotîrlă: Department of Mathematics, Tehnical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania

Mathematics, 2024, vol. 12, issue 24, 1-17

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.

Keywords: bi-univalent functions; (p, q)-derivative operator; subordination; Horodam polynomials; Fekete–Szegö functional (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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