Abstract

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

Keywords: Analytic function; univalent function; integral operator.

MSC: 30C45

Pages:  394--402     

Volume  65 ,  Issue  3 ,  2013