On almost increasing sequences for generalized absolute summability

Creative Commons License

SAVAŞ E.

Mathematical Inequalities and Applications, cilt.9, sa.4, ss.717-723, 2006 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 4
  • Basım Tarihi: 2006
  • Doi Numarası: 10.7153/mia-09-63
  • Dergi Adı: Mathematical Inequalities and Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.717-723
  • Anahtar Kelimeler: Absolute summability, Almost increasing summability factors
  • Uşak Üniversitesi Adresli: Evet

Özet

In this paper, we establish a summability factor theorem for summability |A, δ|k as defined in (2) where A is a lower triangular matrix with non-negative entries satisfying certain conditions. This paper is an extension of the main result of [3] using definition (2) below. Let A be a lower triangular matrix, {sn} a sequence. Then An := ∑v=0nanvsv. A series ∑a n is said to be summable |A|k, k ≥ 1 if ∑n=1∞ nk-1|An - A n-1|k < ∞. (1) and it is said to be summable |A, δ|k, k ≥ 1 and δ ≥ 0 if (see,[1]) ∑n=1∞ nδk+k-1|An - An-1|k < ∞. © ELEMENT.