}$.  Letting $\beta \rightarrow \infty $ in Theorem $\ref{thm0}$, we have the following consequence.  Let $\alpha $ and $\delta $ be real numbers such that $0\leq \alpha ,\delta <0$ and let the function $f\in \mathcal{A}$ be defined by $(\ref{0.0})$. If $f\in \mathcal{B}_{g}\left( \alpha ;\rho \right) $, then$$\left\vert a_{n}\right\vert \leq \left