International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 4, Pages 775-784
The Abel-type transformations into
Department of mathematics, Savannah state university, Savannah 31404, Georgia, USA
Received 24 November 1997; Revised 16 January 1998
Copyright © 1999 Mulatu Lemma. 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.
Let be a sequence in that converges to , and define the Abel-type matrix by for . The matrix determines a sequence-to-sequence variant of the Abel-type power series method of summability introduced by Borwein in . The purpose of
this paper is to study these matrices as mappings into .
Necessary and sufficient conditions for to be -,-, and - are established. Also, the strength of in the - setting is investigated.