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arXiv · 2112.09909

On the Domain of Four-Dimensional Forward Difference Matrix in Some Double Sequence Spaces

Orhan Tug·Eberhard Malkowsky·Vladimir Rakocevic·Bipan Hazarika
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Abstract

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 $\mu=\{\mathcal{M}_u,\mathcal{C}_{\vartheta}\}$.

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Orhan Tug, Eberhard Malkowsky, Vladimir Rakocevic, Bipan Hazarika. 2021-12-18. On the Domain of Four-Dimensional Forward Difference Matrix in Some Double Sequence Spaces. https://arxiv.org/abs/2112.09909

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