Year: 2024
Type: article
Abstract: 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.
Institutions: ICFAI University, Tripura, Tripura University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4403582802