International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 8, Pages 533-538
Matrix transformations from absolutely convergent series to convergent sequences as general weighted mean summability methods
Department of Mathematics, Shawnee State University, Portsmouth 45662, Ohio, USA
Received 10 May 1999; Revised 22 July 1999
Copyright © 2000 Jinlu Li. 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.
We prove the necessary and sufficient conditions for an infinity
matrix to be a mapping, from absolutely convergent series to
convergent sequences, which is treated as general weighted mean
summability methods. The results include a classical result by
Hardy and another by Moricz and Rhoades as particular cases.