On the Fekete-Szegö problem for classes of bi-univalent functions

In this paper we obtain the Fekete-Szegö inequalities for the classes H_σ(φ), ST_σ(α, φ) and M_σ(α, φ) of bi-univalent functions defined in terms of subordination. These inequalities result in the bounds of the third coefficient which improve many known results concerning different classes of bi-univalent functions.