Taylor-Maclaurin coefficients and the Fekete-Szego<spacing diaeresis> inequal- ities for certain subclasses of bi-univalent functions involv- ing the Gegenbauer polynomials

In this paper by using the idea of Gegenbauer polynomials, we introduced certain new subclasses of analytic and biunivalent functions. Additionally, we determined the estimates for first two Taylor-Maclaurin coefficients and the Fekete-Szego center dot functional problems for each of the function classes we defined. In the concluding part, we recall the curious readers attention to the possibility of analyzing the result's q-generalizations presented in this article. Moreover, according to the proposed extension, the (p, q) -extension will only be comparatively small and inconsequently change, as the additional parameter p is redundant.