A characterization of absolute summability factors

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Rhoades B., SAVAŞ E.

Taiwanese Journal of Mathematics, vol.8, no.3, pp.453-465, 2004 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 3
  • Publication Date: 2004
  • Doi Number: 10.11650/twjm/1500407665
  • Journal Name: Taiwanese Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.453-465
  • Keywords: Absolute summability, Summability factors, Weighted mean matrices
  • Uşak University Affiliated: Yes

Abstract

Let A and B be two summability methods. We shall use the notation λ ∈ (A, B) to denote the set of all sequences λ such that ∑a nλn is summable B, whenever ∑an is summable A. In the present paper we characterize the sets λ ∈ (|N̄,pn|, |T|k) and λ ∈ (|N̄,p n|k, |T|), where T is a lower triangular matrix with positive entries and row sums 1. As special cases we obtain summability factor theorems and inclusion theorems for pairs of weighted mean matrices.