The order of convexity for a general integral operator

In this paper, we consider the classes of the univalent functions denoted by $\mathcal{SH}(\beta)$, $\mathcal{SP}$ and $\mathcal{SP}(\alpha,\beta)$. On these classes we study the order of convexity of the integral operator $\int_0^z(te^{f(t)})^\gamma\,dt$, where the function $f$ belongs to these classes.