(untitled) (European Journal of Pure and Applied Mathematics, 2025)
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.