Applications of q- Ultraspherical polynomials to bi-univalent functions defined by q- Saigo's fractional integral operators

This study established upper bounds for the second and third coefficients of analytical and bi-univalent functions belonging to a family of particular classes of analytic functions utilizing q- Ultraspherical polynomials under q- Saigo's fractional integral operator. We also discussed the Fekete-Szegö family function problem. As a result of the specialization of the parameters used in our main results, numerous novel outcomes were demonstrated.