Journal of Mathematical Analysis and Applications, cilt.391, sa.1, ss.67-81, 2012 (SCI-Expanded)
In the present paper, by using generalized weighted mean and difference matrix B, we introduce the paranormed sequence space ℓ(u,v,p;B) which consist of all sequences whose generalized weighted B-difference means are in the linear space ℓ(p) introduced by I.J. Maddox. Also, we give the basis of this space and compute its α-, β- and γ-duals. Further, we characterize the classes of matrix mappings from ℓ(u,v,p;B) to ℓ ∞, c and c 0. Finally, we apply the Hausdorff measure of noncompactness to characterize some classes of compact operators given by matrices on the space ℓp(u,v;B) (1≤p<∞). © 2012 Elsevier Inc.