The problem of V. N. Dubinin for symmetric multiconnected domains
UDC 517.54We consider a quite general problem from the geometric theory of functions on finding a maximal value of the product of the inner radii of $n$ non-overlapping domains, which contain points of the unit circle and are symmetric with respect to the unit circle, and the $\gamma$-powered inner...
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| Datum: | 2020 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2020
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/6064 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.54We consider a quite general problem from the geometric theory of functions on finding a maximal value of the product of the inner radii of $n$ non-overlapping domains, which contain points of the unit circle and are symmetric with respect to the unit circle, and the $\gamma$-powered inner radius of a domain containing the origin. In this paper, we solve this problem for $n\geq 20$ and $1<\gamma\leq n^{\frac{2}{3}-q(n)}.$ |
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| DOI: | 10.37863/umzh.v72i11.6064 |