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

W.T. Sulaiman

Department of Mathematics, College of Science, University of Qatar, Doha, Qatar

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.