Sharp Constant in Jackson’s Inequality with Modulus of Smoothness for Uniform Approximations of Periodic Functions

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dc.contributor.authorPichugov, Sergey A.en
dc.date.accessioned2013-07-02T11:46:51Z
dc.date.available2013-07-02T11:46:51Z
dc.date.issued2012
dc.descriptionS. Pichugov: ORCID 0000-0002-4263-4429en
dc.description.abstractEN: Abstract—It is proved that, in the space C2π, for all k,n ∈ N, n > 1, the following inequalities hold: 1 − 1 2n k2 + 1 2 ≤ sup f∈C2π f=const en−1(f) ω2(f,π/(2nk)) ≤ k2 + 1 2 . where en−1(f) is the value of the best approximation of f by trigonometric polynomials and ω2(f,h) is the modulus of smoothness of f. A similar result is also obtained for approximation by continuous polygonal lines with equidistant nodes.en
dc.identifierDOI: 10.1134/S0001434618110421
dc.identifier.citationPichugov S. A. Sharp Constant in Jackson’s Inequality with Modulus of Smoothness for Uniform Approximations of Periodic Functions / S. A. Pichugov // Mathematical Notes. – 2013. – Vol. 93, № 6. – Р. 116-121. – DOI: 10.1134/S000143461305011.en
dc.identifier.citationPichugov S. A. Sharp Constant in Jackson’s Inequality with Modulus of Smoothness for Uniform Approximations of Periodic Functions. Mathematical Notes. Vol. 93, No. 5-6. P. 917–922. DOI: 10.1134/S0001434618110421. (Russian original Matematicheskie Zametki, 2013, Vol. 93, No. 6, pp. 932–938). Full text.en
dc.identifier.urihttp://eadnurt.diit.edu.ua:82/jspui/handle/123456789/1711
dc.identifier.urihttps://link.springer.com/article/10.1134%2FS0001434613050295
dc.identifier.urihttps://link.springer.com/content/pdf/10.1134%2FS0001434613050295.pdf
dc.language.isoen
dc.publisherPleiades Publishingen
dc.subjectJackson’s inequalityen
dc.subjectperiodic functionen
dc.subjecttrigonometric polynomialen
dc.subjectmodulus of smoothnessen
dc.subjectpolygonal lineen
dc.subjectSteklov meanen
dc.subjectFavard sumen
dc.subjectКПМen
dc.titleSharp Constant in Jackson’s Inequality with Modulus of Smoothness for Uniform Approximations of Periodic Functionsen
dc.typeArticleen
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