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

Ahmad H. A. Bataineh and Laith E. Azar

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 [wθ,M,p,u,Δ]σ, [wθ,M,p,u,Δ]σ0, and [wθ,M,p,u,Δ]σ 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.