Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 451815, 11 pages
doi:10.1155/2008/451815
Research Article

Exact Values of Bernstein n-Widths for Some Classes of Convolution Functions

Feng Guo1,2

1School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
2Department of Mathematics, Taizhou University, Taizhou, Zhejiang 317000, China

Received 10 December 2007; Revised 7 April 2008; Accepted 16 June 2008

Academic Editor: Vijay Gupta

Copyright © 2008 Feng Guo. 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.

Abstract

We consider some classes of 2π-periodic convolution functions B˜p, and K˜p, which include the classical Sobolev class as a special case. With the help of the spectra of nonlinear integral equations, we determine the exact values of Bernstein n-width of the classes B˜p, K˜p in the space Lp for 1<p<∞.