New univalent conditions for a family of integral operators

In this paper, we obtain new sufficient conditions for the operator Gn,α(z)={[n(α−1)+1]∫0z(g1(t))α−1⋯(gn(t))α−1dt}1n(α−1)+1 to be univalent in the open unit disc UU, where each of the functions g1,g2,…,gng1,g2,…,gn satisfy the condition |zgi′(z)gi(z)−a|