International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 3, Pages 197-204
doi:10.1155/S0161171200003811
Abel-type weighted means transformations into ℓ
Savannah State University, Savannah 31404, Georgia, USA
Received 15 July 1999
Copyright © 2000 Mulatu Lemma and George Tessema. 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
Let qk=(k+α k) for α>−1 and Qn=∑k=0nqk. Suppose Aq={ank}, where ank=qk/Qn for 0≤k≤n and 0 otherwise. Aq is called the Abel-type weighted mean matrix. The purpose of this
paper is to study these transformations as mappings into ℓ. A necessary and sufficient condition for Aq to be ℓ-ℓ is proved. Also some other properties of the Aq matrix are investigated.