Coefficient bounds for regular and bi-univalent functions linked with Gegenbauer polynomials

The main goal of the paper is to initiate and explore two sets of regular and bi-univalent (or bi-Schlicht) functions in $\mathfrak{D} =\{z\in\mathbb{C}:|z| <1\}$ linked with Gegenbauer polynomials. We investigate certain coefficient bounds for functions in these families. Continuing the study on the initial coefficients of these families, we obtain the functional of Fekete-Szegö for each of the two families. Furthermore, we present few interesting observations of the results investigated.