On $\mathit{I}$-Statistically Cauchy sequences {&} the class of $\mathit{I}$-statistically concurrent sequences: Real Functions and Algebra

Strany: 111 - 122

In this article, we present the ideas of $I$-statistically Cauchy criteria and $I^*$-statistically Cauchy criteria, which are the generalizations of $I$-Cauchy and $I^*$-Cauchy criterion, respectively. To grasp the differences, we compare this $I$-statistically Cauchy criterion with a few other Cauchy criteria. Also, we investigate a few characteristics of $I^*$-statistically Cauchy sequences and $I$-statistically Cauchy sequences and demonstrate their equivalence under the condition that the ideal $I$ satisfies the property (AP). Furthermore, a relation is defined on the set $S_X$ of all sequences in a metric space, which comes out to be an equivalence relation. Finally, we show that if two sequences belong to the same equivalence class, then either both of them are $I$-statistically Cauchy or none of them are.

ISO 690:

Rakshit, D., Bal, P., Debnath, S. 2024. On $\mathit{I}$-Statistically Cauchy sequences {&} the class of $\mathit{I}$-statistically concurrent sequences: Real Functions and Algebra. In Tatra Mountains Mathematical Publications, vol. 86, no.1, pp. 111-122. 1210-3195. DOI: https://doi.org/0.2478/tmmp-2024-0013

APA:

Rakshit, D., Bal, P., Debnath, S. (2024). On $\mathit{I}$-Statistically Cauchy sequences {&} the class of $\mathit{I}$-statistically concurrent sequences: Real Functions and Algebra. Tatra Mountains Mathematical Publications, 86(1), 111-122. 1210-3195. DOI: https://doi.org/0.2478/tmmp-2024-0013

Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava

https://creativecommons.org/licenses/by-nc-nd/4.0/