International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 2, Pages 55-64

Inclusion results for convolution submethods

Jeffrey A. Osikiewicz1 and Mohammad K. Khan2

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 B is a summability matrix, then the submethod Bλ is the matrix obtained by deleting a set of rows from the matrix B. 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.