×

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.

MSC:

41A30 Approximation by other special function classes
42A10 Trigonometric approximation
PDFBibTeX XMLCite
Full Text: DOI