Abstract and Applied Analysis
Volume 2012 (2012), Article ID 513206, 20 pages
http://dx.doi.org/10.1155/2012/513206
Research Article

On the Convergence of Absolute Summability for Functions of Bounded Variation in Two Variables

Ying Mei1 and Dansheng Yu2

1Department of Mathematics, Lishui University, Lishui, Zhejiang 323000, China
2Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China

Received 25 September 2012; Accepted 12 November 2012

Academic Editor: Jaume Giné

Copyright © 2012 Ying Mei 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.

Abstract

By adopting some new ideas, we obtain the estimates of an absolute convergence for the functions of the bounded variation in two variables. Our results generalize the related results of Humphreys and Bojanic (1999) and Wang and Yu (2003) from one dimension to two dimensions and can be applied to several summability methods.