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Zapiski Nauchnykh Seminarov POMI, 2013, Volume 418, Pages 28–59 (Mi znsl5712)  
On the constants in inequalities of the generalized Jackson theorem type

M. V. Babushkina, V. V. Zhukb

a St. Petersburg National Research University of Information Technologies, Mechanics and Optics, St. Petersburg, Russia
b St. Petersburg State University, St. Petersburg, Russia
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Abstract: Some modifications of Jackson type inequalities are established. These inequalities contain estimates of best approximations of periodical functions by trigonometric polynomials in terms of the moduli of continuity of high orders. Special attention was payed to estimates of constants in the obtained inequalities.
Key words and phrases: best approximation, modulus of continuity, Jackson inequality.
Received: 29.08.2013
English version:
Journal of Mathematical Sciences (New York), 2014, Volume 200, Issue 5, Pages 532–550
DOI: https://doi.org/10.1007/s10958-014-1942-8
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: M. V. Babushkin, V. V. Zhuk, “On the constants in inequalities of the generalized Jackson theorem type”, Analytical theory of numbers and theory of functions. Part 28, Zap. Nauchn. Sem. POMI, 418, POMI, St. Petersburg, 2013, 28–59; J. Math. Sci. (N. Y.), 200:5 (2014), 532–550
Citation in format AMSBIB
\Bibitem{BabZhu13}
\by M.~V.~Babushkin, V.~V.~Zhuk
\paper On the constants in inequalities of the generalized Jackson theorem type
\inbook Analytical theory of numbers and theory of functions. Part~28
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 418
\pages 28--59
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5712}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 200
\issue 5
\pages 532--550
\crossref{https://doi.org/10.1007/s10958-014-1942-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84904174630}
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