On the Domain of Four-Dimensional Forward Difference Matrix in Some Double Sequence Spaces
In this paper, we introduce some new double sequence spaces $\mathcal{M}_u(Δ)$ and $\mathcal{C}_{\vartheta}(Δ)$, where $\vartheta\in\{bp,bp0,r,r0\}$ as the domains of the four-dimensional forward difference matrix in the double sequence spaces $\mathcal{M}_u$ and $\mathcal{C}_{\vartheta}$, respectively. Then we investigate some topological and algebraic properties. Moreover, we determine the $α-$, $β(\vartheta)-$, and $γ-$duals of the new spaces $\mathcal{M}_u(Δ)$ and $\mathcal{C}_{\vartheta}(Δ)$. Finally, we characterize four-dimensional matrix classes $(λ(Δ),μ)$ and $(μ,λ(Δ))$, where $λ=\{\mathcal{M}_u,\mathcal{C}_{\vartheta}\}$ and $μ=\{\mathcal{M}_u,\mathcal{C}_{\vartheta}\}$.
math.FA↗