Serdyuk, A. S.; Ovsij, E. Yu. Approximation of the classes \(C_{\beta}^{\psi}H_{\omega}\) by generalized Zygmund sums. (Russian, English) Zbl 1224.41064 Ukr. Mat. Zh. 61, No. 4, 524-537 (2009); translation in Ukr. Math. J. 61, No. 4, 627-644 (2009). Summary: We obtain asymptotic equalities for the least upper bounds of approximations by Zygmund sums in the uniform metric on the classes of continuous \(2\pi\)-periodic functions whose \((\psi,\beta)\)-derivatives belong to the set \(H_{\omega}\) in the case where the sequences \(\psi\) that generate the classes tend to zero not faster than a power function. Cited in 4 Documents MSC: 41A30 Approximation by other special function classes 42A10 Trigonometric approximation Keywords:approximation; Zygmund sum; periodic function PDFBibTeX XMLCite \textit{A. S. Serdyuk} and \textit{E. Yu. Ovsij}, Ukr. Mat. Zh. 61, No. 4, 524--537 (2009; Zbl 1224.41064); translation in Ukr. Math. J. 61, No. 4, 627--644 (2009) Full Text: DOI