THE ABEL-TYPE TRANSFORMATIONS INTO l

MULATU LEMMA

《International Journal of Mathematics and Mathematical Sciences》 1999卷 (1999/12) Pp. 775-784

https://doi.org/10.1155/S0161171299227755

摘要

Let t be a sequence in (0,1) that converges to 1, and define the Abel-type matrix (The equation is abbreviated). The matrix A_(α,t) determines a sequenceto- sequence variant of the Abel-type power series method of summability introduced by Borwein in [1]. The purpose of this paper is to study these matrices as mappings into l. Necessary and sufficient conditions for A_(α,t) to be l-l, G-l, and G_w-l are established. Also, the strength of A_(α,t) in the l-l setting is investigated.

關鍵字

l-l methods ； l-stronger ； G-G methods ； G_w-G_w methods