Investigating q-Exponential Functions in the Context of Bi-Univalent Functions: Insights into the Fekctc-Szcgö Problem and Second Hankel Determinant

This paper draws inspiration from previous studies and established concepts regarding coefficient estimates within the domains of bi-univalent and analytic functions. In our research, we introduce a novel subclass, which is associated with the q-exponential function. Our investigation focuses on addressing the Fekete-Szego problem within the class, specifically in relation to the q-exponential function. We furnish approximations for the coefficients in question and determine the maximum potential value for the second Hankel determinant. Furthermore, we showcase the accuracy and meticulousness of these discoveries regarding the boundary.