Some New Subclasses of Bi-Univalent Functions Related to Quantum Calculus

The primary objective of this paper is to introduce and investigate several novel subclasses of bi-univalent functions associated with the q-calculus framework. Using appropriate analytical techniques, we derive coefficient bounds for the initial coefficients of the functions belonging to these newly defined classes. In particular, we provide explicit estimates for the second-order Hankel determinant and address the classical Fekete–Szegö functional problem within the context of these classes under suitable conditions. It is important to note that the findings presented in this work not only contribute to the ongoing development of q-analogs in geometric function theory, but also serve as a unifying generalization of many previously known results, which are obtained as special cases of our main findings.