CLASSES OF BI-UNIVALENT FUNCTIONS DEFINED BY CONVOLUTION

In this paper, we introduce two new subclasses of the function class $\Sigma$\ of bi-univalent functions defined in the open unit disc. Furthermore, we find estimates on the coefficient $\left\vert a_{2}\right\vert $ and we obtain the Fekete-Szeg\"o inequalities for certain classes $Q_{\Sigma }\left(\alpha ;\Psi (z)\right) $ and $\mathcal{P}_{\Sigma }\left( \beta ;\Psi(z)\right) $ of \textbf{\ }bi-univalent functions.