Open AccessStrongly $\lambda$-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.