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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, Number 11, Pages 3–22 (Mi ivm9048)  
This article is cited in 12 scientific papers (total in 12 papers)

Inequalities of Kolmogorov's type for derived functions in two variables and application to approximation by an “angle”

S. B. Vakarchuka, A. V. Shvachkob

a Chair of Economic Cybernetics and Mathematical Methods in Economy, Alfred Nobel University of Dnepropetrovsk, 18 Naberezhnaya Lenina str., Dnepropetrovsk, 49000 Unkraine
b Chair of Higher Mathematics, Dnepropetrovsk State Agrarian-Economic University, 25 Voroshilov str., Dnepropetrovsk, 49600 Ukraine
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Abstract: For functions of two variables we obtain sharp inequalities of Kolmogorov's type for partial and mixed intermediate derivatives. We also consider applications of the results to some problems of approximation of functions of two variables by angles and obtain a series of relations which are exact in definite sense.
Keywords: Hermite polynomials, Fourier–Hermite series, inequalities of Kolmogorov's type, the best approximation by angle, generalized polynomial.
Received: 14.03.2014
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2015, Volume 59, Issue 11, Pages 1–18
DOI: https://doi.org/10.3103/S1066369X15110018
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: S. B. Vakarchuk, A. V. Shvachko, “Inequalities of Kolmogorov's type for derived functions in two variables and application to approximation by an “angle””, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 11, 3–22; Russian Math. (Iz. VUZ), 59:11 (2015), 1–18
Citation in format AMSBIB
\Bibitem{VakShv15}
\by S.~B.~Vakarchuk, A.~V.~Shvachko
\paper Inequalities of Kolmogorov's type for derived functions in two variables and application to approximation by an ``angle''
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2015
\issue 11
\pages 3--22
\mathnet{http://mi.mathnet.ru/ivm9048}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2015
\vol 59
\issue 11
\pages 1--18
\crossref{https://doi.org/10.3103/S1066369X15110018}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84945207665}
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
     
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