Applications of q-derivative operator to subclasses of bi-univalent functions involving Gegenbauer polynomials. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Hu, Qiuxia; Shaba, Timilehin Gideon; Younis, Jihad; Khan, Bilal; Mashwani, Wali Khan; Çağlar, Murat
• Is Part Of: Applied mathematics in science and engineering. Volume 30:Issue 1(2022)
• Page Start: 501
• Page End: 520
• Publication Date: 2022-01-02
• Subjects: Analytic and bi-univalent functions -- subordination -- Gegenbauer polynomials -- Hankel determinant -- coefficients bounds -- Fekete–Szegö inequalities; Primary: 30C45 -- 30C50 -- 30C80 -- Secondary:11B65 -- 47B38; Science -- Mathematics -- Periodicals; Engineering mathematics -- Periodicals; Applied mathematics -- Periodicals; 501.51
• DOI: 10.1080/27690911.2022.2088743
• Languages: English
• ISSNs: 2769-0911

Abstract

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.