A Study on Bi-Univalent Functions of Complex Order Arising from the q-Fibonacci Analogue
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i4.7065Keywords:
Classes of bi-univalent functions, Fekete–Szeg¨o operator, Fibonacci numbers, Shell-shaped domains.Abstract
This paper introduces new subclasses of bi-univalent functions of complex order linked with shell-like domains, formulated via the subordination principle and the q-analogue of Fibonacci numbers. Motivated by recent advances in q-calculus and its applications in geometric function theory, we construct and examine two distinct families of analytic bi-univalent
functions. For these subclasses, coefficient estimates are derived for the initial Taylor–Maclaurin coefficients, together with sharp bounds for the Fekete–Szeg¨o functional expressed in terms of the involved parameters. The outcomes of this study extend and unify earlier results in the theory of bi-univalent functions, while providing new insights into the interaction between biunivalent
function theory, the q-Fibonacci framework, and shell-like geometries. Furthermore, the subclasses established here may serve as a foundation for future studies in analytic function spaces, special functions, and their operator-theoretic connections.
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Copyright (c) 2025 Abdullah Alsoboh, Ala Amourah, Khaled Almashrafi, Tala sasa
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