Abel-type weighted means transformations into ℓ. (1st February 2000) - Lemma, Mulatu
Abstract : Letq k = ( k + α k ) forα > − 1 andQ n = ∑ k = 0 n q k . SupposeA q = { a n k }, wherea n k = q k / Q n for0 ≤ k ≤ n and 0 otherwise.A q is called the Abel-type weighted mean matrix. The purpose of this paper is to study these transformations as mappings intoℓ . A necessary and sufficient condition forA q to beℓ -ℓ is proved. Also some other properties of theA q matrix are investigated.