the pioneering work of Srivastava et al.[19], which has actually revived the study of the
coefficient problems involving bi-univalent functions. With motivation from the work of
Srivastava et al.[19], in the present paper we introduce a new subclass TΣ [φ] of the function
class Σ of bi-univalent functions defined in the open unit disk U={z∈ C:| z|< 1}. Further, for
the functions in this subclass TΣ [φ] we obtain bounds on| a2|,| a3| and| a4|.