International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 3, Pages 129-138
doi:10.1155/S0161171202012425

On inclusion relations for absolute summability

B. E. Rhoades1 and Ekrem Savaş2

1Department of Mathematics, Indiana University, Bloomington 47405-7106, IN, USA
2Department of Mathematics, Yüzüncü Yil University, Van, Turkey

Received 15 March 2001; Revised 15 November 2001

Copyright © 2002 B. E. Rhoades and Ekrem Savaş. 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

We obtain necessary and (different) sufficient conditions for a series summable |N¯,pn|k, 1<k≤s<∞, to imply that the series is summable |T|s, where (N¯,pn) is a weighted mean matrix and T is a lower triangular matrix. As corollaries of this result, we obtain several inclusion theorems.