On the univalence of an integral operator

Let U = {z ∈ C : |z| < 1} be the unit disk in the complex plane, and let A be the class of functions which are analytic in the unit disk normalized with f (0) = f ′ (0)− 1 = 0. We denote by P the class of the functions p which are analytic in U , p (0) = 1 and Re p (z) > 0, for all z ∈ U . Let S be the subclass of A, consisting of all univalent functions f in U , and we consider S∗ the subclass of S, consisting of all starlike functions f in U . In this work we introduce a new integral operator, which is defined by