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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.
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.
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