### Estimating coefficients for subclasses of meromorphic bi-univalent functions involving the polylogarithm function

Document Type : Research Paper

Authors

Department of Mathematics, College of Education, Al-Mustansiriyah University, Baghdad, Iraq

Abstract

In this paper, we introduce a new operator $\Omega_{c}\ g(z)$ associated with polylogarithm function, applying it on the subclasses $AH_{\Sigma_{\mathcal{B}}^{*}}(\gamma,k)$ of meromorphic starlike bi-univalent functions of order $\gamma$, and $AH_{{\widetilde{\Sigma}}_{\mathcal{B}}^{*}}(\gamma,k)$ of meromorphic strongly starlike bi-univalent functions of order $\gamma$, also we find estimates on the coefficients $\left| b_{0} \right|$ and $\left| b_{1} \right|$ for functions in these subclasses{.}

Keywords