Recent advances in rough statistical convergence for difference sequences in neutrosophic normed spaces
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This paper expands upon existing theories regarding the convergence of sequences in neutrosophic normed spaces (NNSs) by introducing the concept of rough statistical convergence for difference sequences in NNSs. The study investigates novel notions, namely rough convergence and rough statistical convergence, specifically in the context of difference sequences in NNSs. Furthermore, the paper analyzes various properties and characteristics of a mathematical construct denoted as $St_{\left(\Theta,\Psi,\Omega \right)}-\text{LIM}_{\Delta t_{w}}^{r}$, which is referred to as the $r$-statistical limit set of the difference sequence $\left(\Delta t_{w}\right)$. The examination of these features aims to deepen the understanding of the behavior and attributes associated with the $r$-statistical limit set in the context of rough statistical convergence in NNSs.
Abstract
This paper expands upon existing theories regarding the convergence of sequences in neutrosophic normed spaces (NNSs) by introducing the concept of rough statistical convergence for difference sequences in NNSs. The study investigates novel notions, namely rough convergence and rough statistical convergence, specifically in the context of difference sequences in NNSs. Furthermore, the paper analyzes various properties and characteristics of a mathematical construct denoted as $St_{\left(\Theta,\Psi,\Omega \right)}-\text{LIM}_{\Delta t_{w}}^{r}$, which is referred to as the $r$-statistical limit set of the difference sequence $\left(\Delta t_{w}\right)$. The examination of these features aims to deepen the understanding of the behavior and attributes associated with the $r$-statistical limit set in the context of rough statistical convergence in NNSs.
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