International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 82342, 6 pages

Tauberian conditions for a general limitable method

İbrahım C̣anak and Ümıt Totur

Department of Mathematics, Adnan Menderes University, Aydin 09010, Turkey

Received 16 July 2006; Revised 21 August 2006; Accepted 21 August 2006

Copyright © 2006 İbrahım C̣anak and Ümıt Totur. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let (un) be a sequence of real numbers, L an additive limitable method with some property, and 𝒰 and 𝒱 different spaces of sequences related to each other. We prove that if the classical control modulo of the oscillatory behavior of (un) in 𝒰 is a Tauberian condition for L, then the general control modulo of the oscillatory behavior of integer order m of (un) in 𝒰 or 𝒱 is also a Tauberian condition for L.