International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 11, Pages 1713-1722
Some generalized difference sequence spaces of invariant means
defined by Orlicz functions
Department of Mathematics, Al al-Bayt University, Mafraq 25113, Jordan
Received 23 September 2004; Revised 5 April 2005
Copyright © 2005 Ahmad H. A. Bataineh and Laith E. Azar. 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.
We define the sequence spaces , , and which are defined by combining the concepts of Orlicz functions, invariant means,
and lacunary convergence. We also study some inclusion relations and linearity properties of the above-mentioned spaces. These are generalizations of those defined and studied by
Savaş and Rhoades in 2002 and some others before.