International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 16, Pages 2647-2653
Matrix transformations and Walsh's equiconvergence theorem
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 , for any , as the set of all complex sequences such that . In this paper, we apply 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 matrix transformation of the
difference converges to zero in an arbitrarily large disk. Also,
we give examples of such matrices.