On certain general integral operators of analytic functions

In this paper, we obtain new sufficient conditions for the operators $F_{{\alpha }_1,{\alpha }_2,...,{\alpha }_n,\beta }(z)$ and $G_{{\alpha }_1,{\alpha }_2,...,{\alpha }_n,\beta }(z)$ to be univalent in the open unit disc $\mathcal{U}$, where the functions $f_1,f_2,...,f_n$ belong to the classes $S^{\ast }(a,b)$ and $\mathcal{K}(a,b)$. The order of convexity for the operators $F_{{\alpha }_1,{\alpha }_2,...,{\alpha }_n,\beta }(z)$ and $G_{{\alpha }_1,{\alpha }_2,...,{\alpha }_n,\beta }(z)$ is also determined. Furthermore, and for $\beta =1$, we obtain sufficient conditions for the operators $F_n(z)$ and $G_n(z)$ to be in the class $\mathcal{K}(a,b)$. Several corollaries and consequences of the main results are also considered.