A Novel Subclass of Bi-Univalent Functions Defined by the q-Wright Operator and the q-Analogue of Fibonacci Numbers

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DOI: https://doi.org/10.28924/2291-8639-24-2026-78
Published: Mar 19, 2026
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Abdullah Alsoboh, Ala Amourah, Ahmed Al Kasbi, Jamal Salah, Abed Al-Rahman Malkawi, Tala Sasa, A Novel Subclass of Bi-Univalent Functions Defined by the q-Wright Operator and the q-Analogue of Fibonacci Numbers, Int. J. Anal. Appl., 24 (2026), 78.

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Abdullah Alsoboh, Ala Amourah, Ahmed Al Kasbi, Jamal Salah, Abed Al-Rahman Malkawi, Tala Sasa

Abstract

Inspired by the deep connection between q–calculus and geometric function theory, this study introduces and examines a novel subclass of bi-univalent functions generated through an operator constructed from the q–Wright function and subordinated to the q–analogue of Fibonacci numbers. The core contribution lies in formulating a new q–differential operator defined via convolution with kernels involving the q–Wright function. Employing the subordination principle, the bounds are derived for the initial Taylor–Maclaurin coefficients |a2| and |a3|, along with corresponding Fekete–Szegö type inequalities for the defined class. The presented results not only unify but also generalize various recent developments in the theory of bi-univalent functions, emphasizing the pivotal influence of q–special functions in constructing new analytic frameworks. Consequently, the findings enhance the theoretical understanding of bi-univalent mappings and open avenues for further exploration in operator theory, convolution techniques, and the broader application of q–calculus within complex analysis.

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