Coefficient estimates for a subclass of analytic and bi-univalent functions

Abstract

In the present investigation, we consider a new subclass $\Sigma (\tau \text{,}\gamma \text{,}\phi )$ of the class $\Sigma$ consisting of analytic and bi-univalent functions in the open unit disk $\mathbb{U}$. For functions belonging to the class $\Sigma (\tau \text{,}\gamma \text{,}\phi )$ introduced here, we obtain estimates on the first two Taylor–Maclaurin coefficients $|a_2|$ and $|a_3|$. Several related classes of analytic and bi-univalent functions in $\mathbb{U}$ are also considered and connections to some of the earlier known results are pointed out.