Univalence conditions of general integral operator

Abstract

In this paper, we obtain new univalence conditions for theintegral operator$$I_{\xi }^{{\alpha }_i,{\beta }_i}(f_1,\dots ,f_n)(z)={[\xi ın{t}_0^z{t}^{\xi -1}(f_1^{\prime }(t){)}^{{\alpha }_1}(\frac{f_1(t)}{t}{)}^{{\beta }_1}\cdots (f_n^{\prime }(t){)}^{{\alpha }_n}(\frac{f_n(t)}{t}{)}^{{\beta }_n}dt]}^{\frac{1}{\xi }}$$of analytic functions defined in the open unit disc.