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Exploring Bi-Univalent Classes via q-Derivatives and Bivariate Fibonacci Polynomials

Author

Listed:
  • Aruna Mogarala Guruvaya

    (Department of Artificial Intelligence and Machine Learning, Dayananda Sagar College of Engineering, Bengaluru 560 111, India)

  • Basem Aref Frasin

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

  • Ibtisam Aldawish

    (Mathematics and Statistics Department, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia)

  • Sondekola Rudra Swamy

    (Independent Researcher, Bengaluru 560 098, India)

Abstract

The q -calculus framework has emerged as a powerful tool in geometric function theory, enabling refined analysis of analytic and bi-univalent functions. Inspired by the versatility of the q -derivative operator, this paper introduces a new generalized subclass of bi-univalent functions defined via the q -derivative in combination with generalized bivariate Fibonacci polynomials, which have recently gained significant attention in mathematical research. For functions in this class, we establish bounds on the initial coefficients and provide estimates for the corresponding Fekete–Szegö functional. By appropriate specialization of parameters, our results recover several known findings and, importantly, produce bounds for new subclasses of bi-univalent functions not previously studied. This framework unifies earlier developments while extending the theory to novel, analytically meaningful classes.

Suggested Citation

  • Aruna Mogarala Guruvaya & Basem Aref Frasin & Ibtisam Aldawish & Sondekola Rudra Swamy, 2026. "Exploring Bi-Univalent Classes via q-Derivatives and Bivariate Fibonacci Polynomials," Mathematics, MDPI, vol. 14(4), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:14:y:2026:i:4:p:718-:d:1867697
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