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Russian Mathematical Surveys, 2012, Volume 67, Issue 4, Pages 599–684
DOI: https://doi.org/10.1070/RM2012v067n04ABEH004803 (Mi rm9488) 		 
This article is cited in 26 scientific papers (total in 26 papers)

Methods of geometric function theory in classical and modern problems for polynomials

V. N. Dubinin

Far Eastern Federal University, Vladivostok
English version PDF (1148 kB) Citations (26) Russian version article
References:
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DOI: https://doi.org/10.1070/RM2012v067n04ABEH004803
Abstract: This paper gives a survey of classical and modern theorems on polynomials, proved using methods of geometric function theory. Most of the paper is devoted to results of the author and his students, established by applying majorization principles for holomorphic functions, the theory of univalent functions, the theory of capacities, and symmetrization. Auxiliary results and the proofs of some of the theorems are presented.
Bibliography: 124 titles.
Keywords: majorization principles, Schwarz's lemma, capacities, univalent functions, symmetrization, inequalities, polynomials, critical points, critical values, rational functions.
Received: 12.09.2011
Bibliographic databases:
Document Type: Article
UDC: 517.5
MSC: Primary 30C10; Secondary 30C50, 30C85
Language: English
Original paper language: Russian
Citation: V. N. Dubinin, “Methods of geometric function theory in classical and modern problems for polynomials”, Russian Math. Surveys, 67:4 (2012), 599–684
Citation in format AMSBIB
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\by V.~N.~Dubinin
\paper Methods of geometric function theory in classical and modern problems for polynomials
\jour Russian Math. Surveys
\yr 2012
\vol 67
\issue 4
\pages 599--684
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84868642061}
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  • https://doi.org/10.1070/RM2012v067n04ABEH004803
  • https://www.mathnet.ru/eng/rm/v67/i4/p3
    • This publication is cited in the following 26 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Успехи математических наук Russian Mathematical Surveys
    Statistics & downloads:
    Abstract page:1741
    Russian version PDF:496
    English version PDF:34
    References:146
    First page:96
     
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