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 \(S^*(a, b)\) 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.