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The Koebe set for the class of meromorphic and univalent functions with Montel's normalization - MaRDI portal

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The Koebe set for the class of meromorphic and univalent functions with Montel's normalization (Q1087666)

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scientific article; zbMATH DE number 3987621
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English
The Koebe set for the class of meromorphic and univalent functions with Montel's normalization
scientific article; zbMATH DE number 3987621

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    The Koebe set for the class of meromorphic and univalent functions with Montel's normalization (English)
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    1986
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    Let M(a,p), \(0<| a| <1\), \(0<p<1\) be the class of functions meromorphic and univalent in the unit disk D and normalized by the conditions \[ f(0)=0,\quad f(a)=a,\quad f(p)=\infty. \] The author makes use of connections between M(a,p) and other classes of univalent functions, a result due to \textit{J. Krzyż} [Ann. Univ., Mariae Curie- Skłodowska 15(1961), 57-77 (1962; Zbl 0108.075)] to determine the set \(\cap_{f}f(D)\), \(f\in M(a,p)\).
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