Geodesic
Estimates for functionals with a known moment sequence in terms of deviations of Steklov type means
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 25, Tome 383 (2010), pp. 5-32 
O. L. Vinogradov; V. V. Zhuk. Estimates for functionals with a known moment sequence in terms of deviations of Steklov type means. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 25, Tome 383 (2010), pp. 5-32. http://geodesic.mathdoc.fr/item/ZNSL_2010_383_a0/
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     title = {Estimates for functionals with a~known moment sequence in terms of deviations of {Steklov} type means},
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     year = {2010},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_383_a0/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Some estimates mentioned in the title are established. As implications, Jackson type inequalities with constants smaller than known previously are obtained. The results are valid in different spaces of periodic and non periodic functions. Bibl. 9 titles.

[1] V. V. Zhuk, “O funktsiyakh V. A. Steklova”, Differentsialnye uravneniya s chastnymi proizvodnymi (obschaya teoriya i prilozheniya), Mezhvuz. sb. nauchn. trudov, SPb., 1992, 74–85

[2] V. V. Zhuk, V. F. Kuzyutin, Approksimatsiya funktsii i chislennoe integrirovanie, Izd. S.-Peterburgskogo un-ta, SPb., 1995 | MR | Zbl

[3] S. Foucart, Y. Kryakin, A. Shadrin, “On the exact constant in the Jackson–Stechkin inequality for the uniform metric”, Constr. Approx., 29 (2009), 157–179 | DOI | MR | Zbl

[4] O. L. Vinogradov, V. V. Zhuk, “O konstantakh v obobschennoi teoreme Dzheksona dlya lineinykh metodov priblizheniya”, Teoriya priblizhenii, Tez. dokl. Mezhd. konf. (SPb., 6–8 maya, 2010 g.), SPb., 2010, 9–10 | Zbl

[5] B. M. Levitan, Pochti-periodicheskie funktsii, M., 1953

[6] R. Grekhem, D. Knut, O. Patashnik, Konkretnaya matematika, M., 1998

[7] O. L. Vinogradov, “Tochnye neravenstva tipa Dzheksona dlya priblizhenii klassov svertok tselymi funktsiyami konechnoi stepeni”, Algebra i analiz, 17:4 (2005), 59–114 | MR | Zbl

[8] V. V. Zhuk, Strukturnye svoistva funktsii i tochnost approksimatsii, L., 1984

[9] O. L. Vinogradov, V. V. Zhuk, “Skorost ubyvaniya konstant v neravenstvakh tipa Dzheksona v zavisimosti ot poryadka modulya nepreryvnosti”, Zap. nauchn. semin. POMI, 383, 2010, 33–52