Estimates on Initial Coefficients of Certain Subclasses of bi-univalent Functions Associated with the Class $\mathcal{P}_{m}(\beta)$

Abstract

In this paper, we introduce and investigate certain new subclasses of the function class $\Sigma$ of bi-univalent function defined in the open unit disk, which are associated with the class $\mathcal{P}_{m}(\beta)$. We find estimates on the Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$ for functions in these subclasses. Several known and new consequences of these results are also pointed out in the form of corollaries.