${I}$--Convergence on Cone Metric Spaces
DOI:
https://doi.org/10.5644/SJM.09.1.07Keywords:
Cone metric space, $I$ and $I^*$-convergence, $I$ and $I^*$-Cauchy condition, condition $(AP)$Abstract
The concept of $I$--convergence is an important generalization of statistical convergence which depends on the notion of an ideal $I$ of subsets of the set $\mathbb{N}$ of positive integers. In this paper we introduce the ideas of $I$--Cauchy and $I^*$--Cauchy sequences in cone metric spaces and study their properties. We also investigate the relation between this new Cauchy type condition and the property of completeness.
2000 Mathematics Subject Classification. 40A05, 40D25
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References
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