Tauberian conditions with controlled oscillatory behavior
Articles > Article · 2011
Authors: İbrahim ÇANAK, Umit Totur, Bilender P. Allahverdiev
Applied Mathematics Letters, Journal Indexed in SCI Expanded, International, WoS, 2011, vol 25, pp 252-256
DOI: 10.1016/j.aml.2011.08.017
Summary
Let (u(n)) be a sequence of real numbers. In this paper, we give new Tauberian conditions imposed on the general control modulo of the oscillatory behavior of integer order m >= 1 of a sequence (u(n)), under which, convergence follows from the Abel summability. These are generalizations of some of the well-known classical Tauberian conditions. (C) 2011 Elsevier Ltd. All rights reserved.