Strongly $\lambda$-Statistically and Strongly Vallée-Poussin Pre-Cauchy Sequences in Probabilistic Metric Spaces

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Published: Nov 1, 2022
DOI: https://doi.org/10.5556/j.tkjm.53.2022.3893
Keywords:
Probabilistic metric space strongly λ-statistical convergence strongly λ-statistical pre-Cauchy strongly statistical pre-Cauchy strongly Vall´ee-Poussin pre-Cauchy.

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Argha Ghosh
Brainware University
Samiran Das
The University of Burdwan

Abstract

We introduce the notions of strongly $\lambda$-statistically pre-Cauchy and strongly Vall´ee-Poussin pre-Cauchy sequences in probabilistic metric spaces endowed with strong topology. And we show that these two new notions are equivalent. Strongly $\lambda$-statistically convergent sequences are strongly $\lambda$-statistically pre-Cauchy sequences, and we give an example to show that there is a sequence in a probabilistic metric space which is strongly $\lambda$-statistically pre-Cauchy but not strongly $\lambda$-statistically convergent.

Article Details

How to Cite
Ghosh, A., & Das, S. (2022). Strongly $\lambda$-Statistically and Strongly Vallée-Poussin Pre-Cauchy Sequences in Probabilistic Metric Spaces. Tamkang Journal of Mathematics, 53(4), 373–384. https://doi.org/10.5556/j.tkjm.53.2022.3893
Issue
Vol. 53 No. 4 (2022)
Section
Papers
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This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Author Biography

Samiran Das, The University of Burdwan

Department of Mathematics, Senior Research Fellow. 

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