On strong $\mathcal{A}^{\mathcal{I}}$-statistical convergence of sequences in probabilistic metric spaces

Prasanta Malik; Samiran Das

On strong $\mathcal{A}^{\mathcal{I}}$-statistical convergence of sequences in probabilistic metric spaces

Functional Analysis 2022-08-08 v1

Authors: Prasanta Malik , Samiran Das

Abstract

In this paper using a non-negative regular summability matrix $\mathcal{A}$ and a non-trivial admissible ideal $\mathcal{I}$ in $\mathbb{N}$ we study some basic properties of strong $\mathcal{A}^{\mathcal{I}}$ -statistical convergence and strong $\mathcal{A}^{\mathcal{I}}$ -statistical Cauchyness of sequences in probabilistic metric spaces not done earlier. We also introduce strong $\mathcal{A}^{\mathcal{I^*}}$ -statistical Cauchyness in probabilistic metric space and study its relationship with strong A $\mathcal{A}^{\mathcal{I}}$ -statistical Cauchyness there. Further, we study some basic properties of strong $\mathcal{A}^{\mathcal{I}}$ -statistical limit points and strong $\mathcal{A}^{\mathcal{I}}$ -statistical cluster points of a sequence in probabilistic metric spaces.

Keywords

strong a^i-statistical convergence probabilistic metric spaces summability matrix admissible ideal statistical cauchyness limit points cluster points

Cite

@article{arxiv.2208.03010,
  title  = {On strong $\mathcal{A}^{\mathcal{I}}$-statistical convergence of sequences in probabilistic metric spaces},
  author = {Prasanta Malik and Samiran Das},
  journal= {arXiv preprint arXiv:2208.03010},
  year   = {2022}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2204.02727, arXiv:2007.09173

On strong $\mathcal{A}^{\mathcal{I}}$-statistical convergence of sequences in probabilistic metric spaces

Abstract

Keywords

Cite

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