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Matematicheskie Zametki, 2013, Volume 94, Issue 6, Pages 846–856
DOI: https://doi.org/10.4213/mzm10362 (Mi mzm10362) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Symmetrization of Condensers and Inequalities for Functions Multivalent in a Disk

V. N. Dubininab

a Far Eastern Federal University, Vladivostok
b Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences, Vladivostok
Full-text PDF (472 kB) Citations (5)
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DOI: https://doi.org/10.4213/mzm10362
Abstract: Using the circular symmetrization of sets and condensers on Riemann surfaces, we establish new inequalities for multivalent functions with conditions on the critical values of the functions or on the coverings of concentric circles. Two-point distortion theorems, an inequality for the initial coefficients, and a lower bound for the modulus of functions (of diverse classes) $p$-valent in a disk are proved.
Keywords: circular symmetrization, symmetrization of condensers, multivalent function, two-point distortion theorem, Riemann surface, holomorphic (meromorphic) function.
Received: 07.02.2013
English version:
Mathematical Notes, 2013, Volume 94, Issue 6, Pages 876–884
DOI: https://doi.org/10.1134/S0001434613110242
Bibliographic databases:
Document Type: Article
UDC: 517.54
Language: Russian
Citation: V. N. Dubinin, “Symmetrization of Condensers and Inequalities for Functions Multivalent in a Disk”, Mat. Zametki, 94:6 (2013), 846–856; Math. Notes, 94:6 (2013), 876–884
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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