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
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.