Abstract. In this paper, the generalized differential operator is applied to derive some subclasses of function class  of bi-univalent functions defined in unit disk . We estimate the bounds of the coefficients 2 and 3 for all functions which belong to the derived subclasses of .

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In this paper, we define certain subclasses of analytic univalent function associated with quasi-subordination. Some results such as coefficient bounds and Fekete-Szego bounds for the functions belonging to these subclasses are derived.