Journal of Function Spaces

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Journal of Function Spaces / 2010 / Article

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Volume 8 |Article ID 372106 | 20 pages | https://doi.org/10.1155/2010/372106

On the approximation by trigonometric polynomials in weighted Lorentz spaces

Vakhtang Kokilashvili1 and Yunus E. Yildirir2

1A. Razmadze Mathematical Institute, Aleksidze St. 1, Tbilisi 0193, International Black Sea University, Agmashenebeli Alley 2, Tbilisi 0131, Georgia

2Balikesir University, Faculty of Education, Department of Mathematics, Balikesir, 10100, Turkey

Academic Editor: Henrik Hudzik
Received01 Oct 2008

Abstract

We obtain estimates of structural characteristics of 2π-periodic functions by the best trigonometric approximations in weighted Lorentz spaces, and show that the order of generalized modulus of smoothness depends not only on the rate of the best approximation, but also on the metric of the spaces. In weighted Lorentz spaces Lps, this influence is expressed not only in terms of the parameter p, but also in terms of the second parameter s.

Copyright © 2010 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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