On I -Statistically Cauchy Sequences &amp; the Class of I -Statistically Concurrent Sequences

Rakshit, Debjani; Bal, Prasenjit; Debnath, Shyamal

doi:10.2478/tmmp-2024-0013

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_Xof 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.

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On I -Statistically Cauchy Sequences & the Class of I -Statistically Concurrent Sequences

Abstract

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