Tauberian conditions under which convergence follows from Abel summability


Totur U., ÇANAK İ.

APPLIED MATHEMATICS LETTERS, cilt.23, ss.1439-1443, 2010 (SCI İndekslerine Giren Dergi)

  • Cilt numarası: 23 Konu: 12
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1016/j.aml.2010.07.014
  • Dergi Adı: APPLIED MATHEMATICS LETTERS
  • Sayfa Sayısı: ss.1439-1443

Özet

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.