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

Argha Ghosh | Zendy; Samiran Das | Zendy

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

Author(s) -

Argha Ghosh,

Samiran Das

Publication year - 2021

Publication title -

tamkang journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.324

H-Index - 18

eISSN - 0049-2930

pISSN - 2073-9826

DOI - 10.5556/j.tkjm.53.2022.3893

Subject(s) - mathematics , cauchy sequence , lambda , cauchy distribution , metric space , probabilistic logic , metric (unit) , sequence (biology) , space (punctuation) , pure mathematics , discrete mathematics , combinatorics , topology (electrical circuits) , mathematical analysis , statistics , computer science , physics , operations management , biology , optics , economics , genetics , operating system

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.

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