International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 6, Pages 389-395
doi:10.1155/S016117120100309X
Generalization of some absolute summability methods
Department of Mathematics, College of Science, University of Qatar, Doha, Qatar
Received 6 January 1999
Copyright © 2001 W. T. Sulaiman. 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
Mazhar (1971) gave the characterization for the series ∑anϵn to be summable |N,pn| whenever ∑an is
summable |C,α|k, α≥0, k≥1. Here we prove two
theorems, the first concerns the sufficient conditions and the
second the necessary conditions satisfied by {ϵn} in order to have ∑anϵn summable |N¯,pn|k whenever ∑an is summable |C,α|k, k≥1.