Initial coefficient estimates for subclasses of bi-univalent functions

Abstract

The purpose of the present paper is to introduce new subclasses of the function class $\Sigma$ of normalized analytic and bi-univalent functions in the open disk $\mathbb{U}$. We obtain estimates on the first two Taylor-Maclaurin coefficients $|a_{2}|$ and $|a_{3}|$ for functions of these subclasses.