Novel Bi-Univalent Subclasses Generated by the q-Analogue of the Ruscheweyh Operator and Hermite Polynomials

This work introduces new bi-univalent function classes defined using the fractional q-Ruscheweyh operator and characterized by subordination to q-Hermite polynomials. We derive coefficient bounds and Fekete–Szegö inequalities for these classes and show that our results generalize several earlier findings in both the classical and q-analytic settings. The approach highlights the effectiveness of q-Hermite structures in analyzing operator-defined subclasses of bi-univalent functions.