The study of bi-univalent functions plays an important role in geometric function theory, particularly in determining coefficient bounds for analytic functions. Despite significant progress, there remains a need to develop broader subclasses that allow for more flexible analytical frameworks. Motivated by this, the present work introduces new subclasses of bi-univalent functions defined via generalized bivariate Fibonacci-like polynomials. The proposed classes are constructed using subordination principles and suitable functional relations associated with these polynomials. Based on this approach, estimates for the initial coefficients are derived for functions belonging to the defined subclasses. In addition, Fekete–Szegö inequalities are established, extending several existing results in the literature. The findings demonstrate that the use of generalized Fibonacci-type structures provides an effective tool for obtaining sharper coefficient bounds. These results contribute to the ongoing development of the theory and may serve as a basis for further investigations in related subclasses of analytic and bi-univalent functions.
