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International Journal of Mathematics and Mathematical Sciences
Volume 25, Issue 6, Pages 389-395
http://dx.doi.org/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 Hindawi Publishing Corporation. 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, α0, k1. 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, k1.