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

Abstract

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.

Keywords

• $ q- $ultraspherical polynomials
• univalent functions
• bi-univalent functions
• $ q- $calculus
• analytic functions