Hu, QiuxiaShaba, Timilehin GideonYounis, JihadKhan, BilalMashwani, Wali KhanCaglar, Murat2026-03-262026-03-2620222769-091110.1080/27690911.2022.20887432-s2.0-85137413862https://doi.org/10.1080/27690911.2022.2088743https://hdl.handle.net/20.500.14901/2074Younis, Jihad/0000-0001-7116-3251; Khan, Bilal/0000-0003-2427-2003; Mashwani, Wali Khan/0000-0002-5081-741XIn 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-Szego inequalities and upper bounds for the second-order Hankel determinant for the defined functions class.eninfo:eu-repo/semantics/openAccessAnalytic and Bi-Univalent FunctionsSubordinationGegenbauer PolynomialsHankel DeterminantCoefficients BoundsFekete-Szego InequalitiesArticle