Univalence conditions of general integral operator

Abstract

In this paper, we obtain new univalence conditions for theintegral operator$$I_{\xi}^{\alpha_{i},\beta_{i}}(f_{1},\dots,f_{n})(z)=\left[\xiınt_{0}^{z}t^{\xi-1}(f_{1}^{\prime}(t))^{\alpha_{1}}(\frac{f_{1}(t)}{t})^{\beta_{1}}\cdots(f_{n}^{\prime}(t))^{\alpha_{n}}(\frac{f_{n}(t)}{t})^{\beta_{n}}\,dt\right]^{\frac{1}{\xi}}$$of analytic functions defined in the open unit disc.