×

Trigonometric approximation of functions in \(L _{p}\)-norm. (English) Zbl 1011.42001

This is a very nice paper. The author investigates trigonometric polynomials associated with \(f\in \text{Lip}(\alpha, p)\) (\(0<\alpha\leq 1\), \(p\geq 1\)) to approximate \(f\) in \(L_p\)-norm to the degree of \(O(n^{-\alpha})\) \((0<\alpha\leq 1)\). The most interesting results treat the case \(\alpha= 1\). His three new theorems have numerous attractive corollaries, some of them give sharper estimates than the known ones.

MSC:

42A10 Trigonometric approximation
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Chandra, P., Approximation by Nörlund operators, Mat. Vestnik, 38, 263-269 (1986) · Zbl 0655.42002
[2] Chandra, P., Functions of classes \(L_p\) and Lip \((α,p)\) and their Riesz means, Riv. Mat. Univ. Parma (4), 12, 275-282 (1986) · Zbl 0642.41014
[3] Chandra, P., A note on degree of approximation by Nörlund and Riesz operators, Mat. Vestnik, 42, 9-10 (1990) · Zbl 0725.42004
[4] Mohapatra, R. N.; Russell, D. C., Some direct and inverse theorems in approximation of functions, J. Austral. Math. Soc. (Ser. A), 34, 143-154 (1983) · Zbl 0518.42013
[5] Sahney, B. N.; Rao, V. V.G., Error bounds in the approximation of functions, Bull. Austral. Math. Soc., 6, 11-18 (1972) · Zbl 0229.42008
[6] Quade, E. S., Trigonometric approximation in the mean, Duke Math. J., 3, 529-542 (1937) · Zbl 0017.20501
[7] Zygmund, A., Trigonometric Series, Vol. I (1959), Cambridge University Press: Cambridge University Press Cambridge
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.