On sharp bounds of Fekete-Szego functional for a certain bi-univalent function class associated with quasi-subordination

In the present paper, we introduce a certain subclass K-Sigma(Q)(lambda, gamma, chi) of bi-univalent functions defined in the open unit disk by means of quasi-subordination. Sharp bounds of the initial coefficients vertical bar a(2)vertical bar, vertical bar a(3)vertical bar and the Fekete-Szegfi functional for functions belong to the class K-Sigma(Q)(lambda, gamma, chi) are obtained. Some consequences of these results gives sharp bounds for the subclasses involving subordination, quasi-subordination and majorization.