Estimates on initial coefficients of certain subclasses of bi-univalent functions associated with quasi-subordination

v  In the present investigation we introduce some subclasses of the function class ∑ of bi-univalent functions defined in the open unit disk U, which are associated with the quasi-subordination. We obtain the estimates on initial coefficients |a2| and |a3| for the functions in these subclasses. Also several related subclasses are considered and connection with some known results are established.