Subclasses of bi-univalent functions subordinate to gegenbauer polynomials

In the present paper, we introduce three new classes of bi-univalent functions defined by means of Gegenbauer polynomials. For functions in each of these three bi-univalent function classes, we have derived the estimates of the Taylor–Maclaurin coefficients a 2 and a 3 and Fekete–Szegö functional problems for functions belonging to these new subclasses. A number of new results are shown to follow upon specializing the parameters involved in our main results.