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

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.