International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 16, Pages 2647-2653

Matrix transformations and Walsh's equiconvergence theorem

Chikkanna R. Selvaraj and Suguna Selvaraj

Pennsylvania State University, Shenango Campus 147, Shenango Avenue Sharon, 16146, PA, USA

Received 13 January 2005; Revised 25 March 2005

Copyright © 2005 Chikkanna R. Selvaraj and Suguna Selvaraj. 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.


In 1977, Jacob defines Gα, for any 0α<, as the set of all complex sequences x such that |xk|1/kα. In this paper, we apply GuGv matrix transformation on the sequences of operators given in the famous Walsh's equiconvergence theorem, where we have that the difference of two sequences of operators converges to zero in a disk. We show that the GuGv matrix transformation of the difference converges to zero in an arbitrarily large disk. Also, we give examples of such matrices.