On the mth order difference sequence space of generalized weighted mean and compact operators

In this article, using generalized weighted mean and difference matrix of order m, we introduce the paranormed sequence space ℓ(u, v, p; Δ(m)), which consist of the sequences whose generalized weighted Δ(m)-difference means are in the linear space ℓ(p) defined by I.J. Maddox. Also, we determine the basis of this space and compute its α-, β- and γ-duals. Further, we give the characterization of the classes of matrix mappings from ℓ(u, v, p, Δ(m)) to ℓ∞, c and c0. Finally, we apply the Hausdorff measure of noncompacness to characterize some classes of compact operators given by matrices on the space ℓp(u, v, Δ(m))(1 ≤ p < ∞).