Hankel Determinant Estimates for Bi-Bazilevič-Type Functions Involving q-Fibonacci Numbers

This study focuses on a specific class of analytic and bi-univalent functions of Bazilevič-type, formulated within a geometric context shaped by shell-like curves and influenced by the q-analogue of Fibonacci numbers. By utilizing the subordination approach, we establish precise bounds for the initial coefficients in the Taylor–Maclaurin expansion of these functions. Moreover, the paper presents Fekete–Szegö-type inequalities and introduces novel bounds for the second Hankel determinant, thereby contributing to a deeper analytical insight into the behavior of this function class. These contributions not only broaden the scope of traditional coefficient problems related to bi-univalent functions but also highlight the intricate connections among geometric function theory, specialized function classes, and the principles of q-calculus. The outcomes pave the way for future studies aimed at deriving bounds for higher-order coefficients and examining determinant-related functionals under this theoretical model.