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Zapiski Nauchnykh Seminarov POMI, 2002, Volume 286, Pages 74–84 (Mi znsl1568)  
This article is cited in 59 scientific papers (total in 59 papers)

On the Shwarz inequality on the boundary for functions regular in the disk

V. N. Dubinin

Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences
Full-text PDF (191 kB) Citations (59)
Abstract: The classical Schwarz inequality on the boundary of the disk for the functions regular in the disk is refined in various directions. Inequalities involving zeros of the function, an inequality for points mapped to symmetric points on the circle, and an inverse estimate for univalent functions are presented. Other inequalities are discussed, and the possibility of applying them to estimates of polynomials and rational functions is indicated.
Received: 15.04.2002
English version:
Journal of Mathematical Sciences (New York), 2004, Volume 122, Issue 6, Pages 3623–3629
DOI: https://doi.org/10.1023/B:JOTH.0000035237.43977.39
Bibliographic databases:
UDC: 517.54
Language: Russian
Citation: V. N. Dubinin, “On the Shwarz inequality on the boundary for functions regular in the disk”, Analytical theory of numbers and theory of functions. Part 18, Zap. Nauchn. Sem. POMI, 286, POMI, St. Petersburg, 2002, 74–84; J. Math. Sci. (N. Y.), 122:6 (2004), 3623–3629
Citation in format AMSBIB
\Bibitem{Dub02}
\by V.~N.~Dubinin
\paper On the Shwarz inequality on the boundary for functions regular in the disk
\inbook Analytical theory of numbers and theory of functions. Part~18
\serial Zap. Nauchn. Sem. POMI
\yr 2002
\vol 286
\pages 74--84
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1568}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1937369}
\zmath{https://zbmath.org/?q=an:1070.30008}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2004
\vol 122
\issue 6
\pages 3623--3629
\crossref{https://doi.org/10.1023/B:JOTH.0000035237.43977.39}
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    • This publication is cited in the following 59 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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