Applications of q-derivative operator to subclasses of bi-univalent functions involving Gegenbauer polynomials. Issue 1 (2nd January 2022) - Hu, Qiuxia; Shaba, Timilehin Gideon; Younis, Jihad; Khan, Bilal; Mashwani, Wali Khan; Çağlar, Murat
ABSTRACT: In recent years, using the idea of analytic and bi-univalent functions, many ideas have been developed by different well-known authors, but the using Gegenbauer polynomials along with certain bi-univalent functions is very rare in the literature. We are essentially motivated by this recent research going on, here in our present investigation, we make use of certain q -derivative operator and Gegenbauer polynomials and define a new subclass of analytic and bi-univalent functions. We then obtain certain coefficient bounds, the Fekete–Szegö inequalities and upper bounds for the second-order Hankel determinant for the defined functions class.