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

Key Points

• The aim is to introduce novel classes of bi-univalent functions defined by the q-Ruscheweyh operator and to analyze their properties.
• Defined new bi-univalent function classes using the fractional q-Ruscheweyh operator.
• Characterized these classes via subordination to q-Hermite polynomials.
• Derived coefficient bounds and examined Fekete–Szegö inequalities.
• Generalized several findings from classical and q-analytic settings.
• Established new coefficient bounds for bi-univalent functions.
• Highlighted the effectiveness of q-Hermite structures in analyzing these subclasses.

Abstract