International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 2, Pages 55-64
Inclusion results for convolution submethods
1Department of Mathematical Sciences, Kent State University, Tuscarawas Campus, 330 University Dr. NE, New Philadelphia 44663-9403, OH, USA
2Department of Mathematical Sciences, Kent State University, Kent 44242-0001, OH, USA
Received 30 January 2003; Revised 9 June 2003
Copyright © 2004 Jeffrey A. Osikiewicz and Mohammad K. Khan. 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.
If is a summability matrix, then the submethod is
the matrix obtained by deleting a set of rows from the matrix
. Comparisons between Euler-Knopp submethods and the Borel
summability method are made. Also, an equivalence result for
convolution submethods is established. This result will
necessarily apply to the submethods of the Euler-Knopp, Taylor,
Meyer-König, and Borel matrix summability methods.