International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 15, Pages 2491-2496
doi:10.1155/IJMMS.2005.2491
On a theorem of W. Meyer-König and H. Tietz
1Department of Mathematics, Faculty of Arts and Sciences, Adnan Menderes University, Aydin 09010, Turkey
2Department of Mathematics, Rockford College, 5050 E. State Street, Rockford, IL 61108, USA
3Department of Mathematics and Computer Science, Edgewood College, 1000 Edgewood College Drive, Madison, WI 53711, USA
Received 1 February 2005; Revised 9 March 2005
Copyright © 2005 İBrahım Çanak et al. 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.
Abstract
Let (un) be a sequence of real numbers and let L be an additive limitable method with some property. We prove that if the classical control modulo of the oscillatory behavior of (un) belonging to some class of sequences is a Tauberian condition for L, then convergence or subsequential convergence of (un) out of L is recovered depending on the conditions on the general control modulo of the oscillatory behavior of different order.