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 Tr. Mat. Inst. Steklova, 2010, Volume 269, Pages 150–152 (Mi tm2901)

This article is cited in 2 scientific papers (total in 2 papers)

On the second moduli of continuity

S. V. Konyagin

Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

Abstract: We prove an inequality for the second moduli of continuity of continuous functions. Applying this inequality, we construct a nonnegative nonincreasing continuous function $\omega$ on $[0,+\infty)$ that vanishes at zero and is such that the function $\omega(\delta)/\delta^2$ decreases on $(0,+\infty)$ while $\omega$ is not asymptotically (as $\delta\to0$) equivalent to the second modulus of continuity of any continuous function.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2010, 269, 143–145

Bibliographic databases:

Document Type: Article
UDC: 517.518.2
Received in September 2009

Citation: S. V. Konyagin, “On the second moduli of continuity”, Function theory and differential equations, Collected papers. Dedicated to Academician Sergei Mikhailovich Nikol'skii on the occasion of his 105th birthday, Tr. Mat. Inst. Steklova, 269, MAIK Nauka/Interperiodica, Moscow, 2010, 150–152; Proc. Steklov Inst. Math., 269 (2010), 143–145

Citation in format AMSBIB
\Bibitem{Kon10} \by S.~V.~Konyagin \paper On the second moduli of continuity \inbook Function theory and differential equations \bookinfo Collected papers. Dedicated to Academician Sergei Mikhailovich Nikol'skii on the occasion of his 105th birthday \serial Tr. Mat. Inst. Steklova \yr 2010 \vol 269 \pages 150--152 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm2901} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2729980} \zmath{https://zbmath.org/?q=an:1207.26026} \elib{http://elibrary.ru/item.asp?id=15109758} \transl \jour Proc. Steklov Inst. Math. \yr 2010 \vol 269 \pages 143--145 \crossref{https://doi.org/10.1134/S0081543810020124} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000281705900012} \elib{http://elibrary.ru/item.asp?id=15337080} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77956625009} 

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This publication is cited in the following articles:
1. Bezkryla S.I., Nesterenko O.N., Chaikovs'kyi A.V., “on the Third Moduli of Continuity”, Ukr. Math. J., 66:10 (2015), 1589–1594
2. Bezkryla S.I., Nesterenko O.N., Chaikovs'kyi A.V., “On High Orders Moduli of Continuity Generated By Semigroups of Operators”, Jaen J. Approx., 8:2 (2016), 183–190
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