On the B-difference sequence space derived by generalized weighted mean and compact operators

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 ℓ p ( u , v ; B ) ( 1 ⩽ p < ∞ ).