Measure of noncompactness of matrix operators on some difference sequence spaces of weighted means

For a sequence x=(xk)x=(xk), we denote the difference sequence by Δx=(xk−xk−1)Δx=(xk−xk−1). Let u=(uk)k=0∞ and v=(vk)k=0∞ be the sequences of real numbers such that uk≠0uk≠0, vk≠0vk≠0 for all k∈Nk∈N. The difference sequence spaces of weighted means λ(u,v,Δ)λ(u,v,Δ) are defined as λ(u,v,Δ)={x=(xk):W(x)∈λ},λ(u,v,Δ)={x=(xk):W(x)∈λ}, where λ=c,c0λ=c,c0 and ℓ∞ℓ∞ and the matrix W=(wnk)W=(wnk) is defined by wnk={un(vk−vk+1);(kn). In this paper, we establish some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain matrix operators on λ(u,v,Δ)λ(u,v,Δ). Further, we characterize some classes of compact operators on these spaces by using the Hausdorff measure of noncompactness.