Bi-Starlike and Bi-Convex Function Classes Connected to Shell-Like Curves and the q-Analogue of Fibonacci Numbers

Using the subordination principle, this study explores two subclasses of bi-univalent functions associated with shell-like curves via the q-analogue of Fibonacci numbers, namely the starlike and convex classes. We derive coefficient bounds for the initial terms of these function classes and establish the corresponding Fekete- Szegö inequalities. Our findings contribute to the advancement of biunivalent function theory and its interaction with special function spaces.