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The purpose of the present paper is to introduce a new subclasses of thefunction class of bi-univalent functions defined in the open unit disc.Furthermore, we obtain estimates on the coefficients $|a_{2}|$ and $|a_{3}|$for functions of this class. Some results related to this work will be brieflyindicated.

On the coefficient of The $n^{th}$ Cesaro mean of order $\alpha$ of bi-univalent functions