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

İBrahım Çanak,1 Mehmet Dık,2 and Fılız Dık3

 1Department of Mathematics, Faculty of Arts and Sciences, Adnan Menderes University, Aydin 09010, Turkey
2Department of Mathematics, Rockford College, 5050 E. State Street, Rockford 61108, IL, USA
3Department of Mathematics and Computer Science, Edgewood College, 1000 Edgewood College Drive, Madison 53711, WI, USA
Received 1 February 2005; Revised 9 March 2005

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.