  \[thm0\]Let $\alpha ,\beta $ and $\delta $ be real numbers such that $0\leq \alpha ,\delta <0<\beta $ and let the function $f\in \mathcal{A}$ be defined by $(\ref{0.0})$. If $f\in \mathcal{B}_{g}\left( \alpha ,\beta ;\rho \right) $, then$$\begin{aligned} \left\vert a_{n}\right\vert 