Kaplan classes of a certain family of functions

Szymon Ignaciuk, Maciej Parol


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.


Kaplan classes; univalence; close-to-convex functions; critical points

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DOI: http://dx.doi.org/10.17951/a.2020.74.2.31-40
Data publikacji: 2020-12-28 17:41:58
Data złożenia artykułu: 2020-12-27 16:49:42


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