Table of Contents
ISRN Mathematical Analysis
Volume 2014 (2014), Article ID 713175, 14 pages
Research Article

Approximation by -Transformation of Double Walsh-Fourier Series to Multivariable Functions

1Department of Mathematics, Hangzhou Dianzi University, Hangzhou, Zhejiang 310018, China
2Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China

Received 20 January 2014; Accepted 9 March 2014; Published 22 April 2014

Academic Editors: D. G. Costa, C. Gutiérrez, and D.-X. Zhou

Copyright © 2014 Yi Zhao and Dansheng Yu. 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.


We study the Walsh series expansion of multivariate functions in and, in particular, in . The rate of uniform approximation by T-transformation of rectangular partial sums of double Walsh to these functions is investigated. By extending the concepts of rest (head) bounded variation series, which was introduced by Leindler (2004), we generalize the related results of Móricz and Rhoades (1996), Nagy (2012). Our results can be applied to many summability methods, including the Nörlund summability and weighted summability.