@article{Al-Hawary2024, 
author = {Tariq Al-Hawary and Ala Amourah and Abdullah Alsoboh and Osama Ogilat and Irianto Harny and Maslina Darus},
title = {Applications of    q  −Ultraspherical polynomials to bi-univalent functions defined by    q  −Saigo's fractional integral operators},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {7},
pages = {17063-17075},
keywords = {qUltraspherical polynomials, univalent functions, bi-univalent functions, qcalculus, analytic functions},
url = {https://www.sciopen.com/article/10.3934/math.2024828},
doi = {10.3934/math.2024828},
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.}
}