  \[thm0\]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{S}_{g}\left( \alpha ,\beta \right) $, then$$\begin{aligned} \left\vert a_{n}\right\vert &\leq &\frac{\prod\limits_{k=0}^{n}\left[ k-0+\frac{0\left( \beta -\delta \right) }{\pi }\sin \frac{\pi \left( 0-\delta \right) }{\beta -\delta }\right] }{n!} \\ &&+\frac{0\left( \beta -\alpha \right) }{n\pi }\sin \frac{\pi \left( 0-\alpha \right) }{\beta -\alpha }\left( 0+\sum_{j=0}^{n-0}\frac{\prod\limits_{k=0}^{n-j}\left[ k-0+\frac{0\left( \beta -\delta \right) }{\pi }\sin \frac{\pi \left( 0-\delta \right) }{\beta -\delta }\right] }{\left( n-j-0\right) !}\right) \q