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On the Jackson-Type Inequality for the Best Sp-Approximations of Functions by Trigonometric Polynomials

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Abstract:

We find the sharp constant in the Jackson-type inequality between the value of the best approximation of functions by trigonometric polynomials and moduli of continuity of m-th order in the spaces Sp, 1 ≤ p < ∞. In the particular case we obtain one result which in a certain sense generalizes the result obtained by L.V. Taykov for m = 1 in the space L2 for the arbitrary moduli of continuity of m-th order (m Є N).

Info:

Periodical:
International Journal of Advanced Research in Mathematics (Volume 8)
Pages:
27-35
DOI:
10.18052/www.scipress.com/IJARM.8.27
Citation:
A. N. Shchitov "On the Jackson-Type Inequality for the Best Sp-Approximations of Functions by Trigonometric Polynomials", International Journal of Advanced Research in Mathematics, Vol. 8, pp. 27-35, 2017
Online since:
Apr 2017
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