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 Zap. Nauchn. Sem. POMI, 2010, Volume 383, Pages 33–52 (Mi znsl3870)

The rate of decrease of constants in Jackson type inequalities in dependence of the order of modulus of continuity

O. L. Vinogradov, V. V. Zhuk

St. Petersburg State University, St. Petersburg, Russia

Abstract: Jackson type inequalities for moduli of continuity of arbitrary order are established with the use of linear approximation methods. The constants are smaller than known previously. The results are valid in different spaces of periodic and non periodic functions. Bibl. 19 titles.

Key words and phrases: best approximation, modulus of continuity, sharp constants.

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Document Type: Article
UDC: 517.5

Citation: O. L. Vinogradov, V. V. Zhuk, “The rate of decrease of constants in Jackson type inequalities in dependence of the order of modulus of continuity”, Analytical theory of numbers and theory of functions. Part 25, Zap. Nauchn. Sem. POMI, 383, POMI, St. Petersburg, 2010, 33–52

Citation in format AMSBIB
\Bibitem{VinZhu10} \by O.~L.~Vinogradov, V.~V.~Zhuk \paper The rate of decrease of constants in Jackson type inequalities in dependence of the order of modulus of continuity \inbook Analytical theory of numbers and theory of functions. Part~25 \serial Zap. Nauchn. Sem. POMI \yr 2010 \vol 383 \pages 33--52 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl3870} 

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This publication is cited in the following articles:
1. O. L. Vinogradov, V. V. Zhuk, “Estimates for functionals with a known moment sequence in terms of deviations of Steklov type means”, J. Math. Sci. (N. Y.), 178:2 (2011), 115–131
2. O. L. Vinogradov, V. V. Zhuk, “Estimates for functionals with a known finite set of moments in terms of deviations of operators constructed with the use of the Steklov averages and finite differences”, J. Math. Sci. (N. Y.), 184:6 (2012), 679–698
3. O. L. Vinogradov, “Sharp estimates of best approximations in terms of holomorphic functions of Weierstrass-type operators”, J. Math. Sci. (N. Y.), 193:1 (2013), 8–31
4. V. V. Zhuk, “Inequalities of type generalized Jackson theorem for best approximations”, J. Math. Sci. (N. Y.), 193:1 (2013), 75–88
5. O. L. Vinogradov, V. V. Zhuk, “Estimates for functional with a known finite set of moments in terms of moduli of continuity and behaviour of constants in the Jackson-type inequalities”, St. Petersburg Math. J., 24:5 (2013), 691–721
6. O. L. Vinogradov, V. V. Zhuk, “Estimates for functionals with a known finite set of moments in terms of high order moduli of continuity in the spaces of functions defined on the segment”, St. Petersburg Math. J., 25:3 (2014), 421–446
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