International Journal of Mathematics and Mathematical Sciences 
Volume 2006 (2006), Article ID 82342, 6 pages
doi:10.1155/IJMMS/2006/82342

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

Abstract

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.