International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 11, Pages 1713-1722
doi:10.1155/IJMMS.2005.1713

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

Abstract

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.