Tauberian conditions under which convergence follows from Abel summability


Totur U., ÇANAK İ.

APPLIED MATHEMATICS LETTERS, vol.23, no.12, pp.1439-1443, 2010 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 23 Issue: 12
  • Publication Date: 2010
  • Doi Number: 10.1016/j.aml.2010.07.014
  • Title of Journal : APPLIED MATHEMATICS LETTERS
  • Page Numbers: pp.1439-1443

Abstract

In this work we prove that one-sided slow oscillation of a sequence and that of its generator sequence are Tauberian conditions for the Abel summability method, using a corollary to Karamata's Main Theorem [J. Karamata, Uber die Hardy-Littlewoodschen Umkehrungen des Abelschen Stetigkeitssatzes, Math. Z. 32 (1930) 319-320]. It is also shown that such conditions are Tauberian conditions for generalized Abelian summability methods. (C) 2010 Elsevier Ltd. All rights reserved.