On the Domain of Four-Dimensional Forward Difference Matrix in Some Double Sequence Spaces
| Autor: | Tug, Orhan, Malkowsky, Eberhard, Rakocevic, Vladimir, Hazarika, Bipan |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we introduce some new double sequence spaces $\mathcal{M}_u(\Delta)$ and $\mathcal{C}_{\vartheta}(\Delta)$, 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 $\alpha-$, $\beta(\vartheta)-$, and $\gamma-$duals of the new spaces $\mathcal{M}_u(\Delta)$ and $\mathcal{C}_{\vartheta}(\Delta)$. Finally, we characterize four-dimensional matrix classes $(\lambda(\Delta),\mu)$ and $(\mu,\lambda(\Delta))$, where $\lambda=\{\mathcal{M}_u,\mathcal{C}_{\vartheta}\}$ and $\mu=\{\mathcal{M}_u,\mathcal{C}_{\vartheta}\}$. Comment: 18 pages, 2 tables |
| Databáze: | arXiv |
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