Abstract
In the current study, we provide a novel qualitative new subclass of analytical and biunivalent functions in the symmetry domain U defined by the use of Gegenbauer polynomials. We derive estimates for the Fekete-Szego functional problems and the Taylor-Maclaurin coefficients |a(2)| and |a(3)| for the functions that belong to each of these new subclasses of the bi-univalent function classes. Some more results are revealed after concentrating on the parameters employed in our main results.