Univalence of certain integral opertors (Q1578367)

Let \(S\) be the usual class of normalized univalent functions in the unit disc \(U\). Many authors studied the problem of univalence of integral operators which preserves the class \(S\). The author quotes some examples (Theorem 1.1, Theorem 1.2, Theorem 2.1). Theorem 3.1 is another example of this kind proved by the author. The same is true for the (more complicated) Theorem 3.2. Methods of proofs are direct. The authors do not discuss the question of sharpness.