A certain differential operator $ I_{λ}^{m}f(z) $ is introduced for functions of the form $f(z)=(1/(z^{p}))+∑_{n=k}^{∞}a_{n+p-1}z^{n+p-1} $ which are $p$-valent in the punctured unit disk $U^{ }={z:z∈C ext{ and } 0<|z|<1},$ where $p$ and $ k $ are positive integers. The main object of this paper is to give an application of the operator $I_{λ}^{m}f(z)$ to the differential inequalities.