Tauberian conditions under which convergence follows from Abel summability
Articles > Article · 2010
Authors: Umit Totur, İbrahim ÇANAK
Applied Mathematics Letters, Journal Indexed in SCI Expanded, International, WoS, 2010, vol 23, pp 1439-1443
DOI: 10.1016/j.aml.2010.07.014
Summary
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.