New Families of Bi-Univalent Functions Governed by Gegenbauer Polynomials

The aim of this article is to initiating an exploration of the properties of bi-univalent functions related to Gegenbauer polynomials. To do so, we introduce a new families T_Σ (γ, φ, μ, η, θ, , t, δ) and S_Σ (σ, η, θ, , t, δ ) of holomorphic and bi-univalent functions. We derive estimates on the initial coefficients and solve the Fekete-Szeg problem of functions in these families.