Pichugov, Sergey A.2013-07-022013-07-022012Pichugov 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.Pichugov 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.http://eadnurt.diit.edu.ua:82/jspui/handle/123456789/1711https://link.springer.com/article/10.1134%2FS0001434613050295https://link.springer.com/content/pdf/10.1134%2FS0001434613050295.pdfS. Pichugov: ORCID 0000-0002-4263-4429EN: 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.enJackson’s inequalityperiodic functiontrigonometric polynomialmodulus of smoothnesspolygonal lineSteklov meanFavard sumКПМArticle