Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 475320, 12 pages
doi:10.1155/2009/475320
Research Article

The Average Errors for the Grünwald Interpolation in the Wiener Space

Yingfang Du1 and Huajie Zhao2

1College of Chemistry and Life Science, Tianjin Normal University, Tianjin 300387, China
2Department of Mathematics, Tianjin Normal University, Tianjin 300387, China

Received 15 May 2009; Accepted 10 June 2009

Academic Editor: Guang Zhang

Copyright © 2009 Yingfang Du and Huajie Zhao. 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 determine the weakly asymptotically orders for the average errors of the Grünwald interpolation sequences based on the Tchebycheff nodes in the Wiener space. By these results we know that for the Lp-norm (2≤q≤4) approximation, the p-average (1≤p≤4) error of some Grünwald interpolation sequences is weakly equivalent to the p-average errors of the best polynomial approximation sequence.