A characterization of absolute summability factors

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Rhoades B., SAVAŞ E.

Taiwanese Journal of Mathematics, cilt.8, sa.3, ss.453-465, 2004 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 8 Sayı: 3
  • Basım Tarihi: 2004
  • Doi Numarası: 10.11650/twjm/1500407665
  • Dergi Adı: Taiwanese Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.453-465
  • Anahtar Kelimeler: Absolute summability, Summability factors, Weighted mean matrices
  • Uşak Üniversitesi Adresli: Evet

Özet

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.