Open AccessKaplan classes of a certain family of functions
Author(s) -
Szymon Ignaciuk,
Maciej Parol
Publication year - 2020
Publication title -
annales universitatis mariae curie-skłodowska. sectio a, mathematica
Language(s) - English
Resource type - Journals
eISSN - 2083-7402
pISSN - 0365-1029
DOI - 10.17951/a.2020.74.2.31-40
Subject(s) - monotonic function , characterization (materials science) , sequence (biology) , mathematics , power (physics) , class (philosophy) , combinatorics , pure mathematics , discrete mathematics , function (biology) , physics , mathematical analysis , computer science , chemistry , quantum mechanics , biochemistry , artificial intelligence , optics , evolutionary biology , biology
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.