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Matematicheskie Zametki, 2020, Volume 107, Issue 6, Pages 865–872
DOI: https://doi.org/10.4213/mzm12756 (Mi mzm12756) 		 
This article is cited in 1 scientific paper (total in 1 paper)

The Schwarzian Derivative of a $p$-Valent Function

V. N. Dubininab

a Far Eastern Federal University, Vladivostok
b Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok
Full-text PDF (448 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm12756
Abstract: We show that a comparison of the capacities of suitable condensers gives an inequality for the Schwarzian derivatives of a holomorphic $p$-valent function defined on the unit disk and ranging in a given domain of the complex plane. If that domain is a disk as well and the function is univalent, then this inequality essentially coincides with the classical Nehari inequality. The cases of equality in the resulting relation are discussed.
Keywords: Schwarzian derivative, $p$-valent function, holomorphic function, condenser capacity, Green's function.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00018
Ministry of Education and Science of the Russian Federation 075-01095-20-00
This work was carried out in the framework of the Russian State Assignment (grant no. 075-01095-20-00) and supported in part by the Russian Foundation for Basic Research under grant no. 20-01-00018.
Received: 20.01.2020
English version:
Mathematical Notes, 2020, Volume 107, Issue 6, Pages 953–958
DOI: https://doi.org/10.1134/S0001434620050260
Bibliographic databases:
Document Type: Article
UDC: 517.54
Language: Russian
Citation: V. N. Dubinin, “The Schwarzian Derivative of a $p$-Valent Function”, Mat. Zametki, 107:6 (2020), 865–872; Math. Notes, 107:6 (2020), 953–958
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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