A summability factor theorem and applications

Rhoades B., SAVAŞ E.

Applied Mathematics and Computation, vol.153, no.1, pp.155-163, 2004 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 153 Issue: 1
  • Publication Date: 2004
  • Doi Number: 10.1016/s0096-3003(03)00620-9
  • Journal Name: Applied Mathematics and Computation
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.155-163
  • Keywords: Absolute summability, Cesáro matrix, Summability factor, Weighted mean matrix
  • Uşak University Affiliated: Yes

Abstract

We obtain sufficient conditions for the series ∑an, which is absolutely summable of order k by a weighted mean method, to be such that ∑εnan is absolutely summable of order k by a triangular matrix. As corollaries we obtain a number of inclusion theorems. © 2003 Elsevier Inc. All rights reserved.