In this article we consider the problem of univalence of a function introduced by Breaz and Ularu, improve some of their results and receive not only univalence conditions but also close-to-convex conditions for this function. To this aim, we used our method based on Kaplan classes.
We give the complete characterization of members of Kaplan classes of products of power functions with all zeros symmetrically distributed in \(\mathbb{T} := \{z \in\mathbb{C} : |z| = 1\}\) and weakly monotonic sequence of powers. In this way we extend Sheil-Small’s theorem. We apply the obtained result to study univalence of antiderivative of these products of power functions.
Criteria of univalence for a certain integral operator
