Abstract

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.

Keywords and Phrases

Bi-univalent, Fekete-Szego, Hadamard product.

A.M.S. subject classification

Primary 30C45, Secondary 30C50.

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