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