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

In this paper we obtain the Fekete-Szego inequalities for the classes H-sigma(phi), ST sigma(alpha, phi) and M-sigma(alpha, phi) 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 hi-univalent functions.