Taiwanese Journal of Mathematics

ON $\mathcal{I}$-CAUCHY SEQUENCES

Anar Nabiev, Serpil Pehlivan, and Mehmet Gürdal

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Abstract

The concept of $\mathcal{I}$-convergence is a generalization of statistical convergence and it is dependent on the notion of the ideal $\mathcal{I}$ of subsets of the set $\mathbb{N}$ of positive integers. In this paper we prove a decomposition theorem for $\mathcal{I}$-convergent sequences and we introduce the notions of $\mathcal{I}$ Cauchy sequence and $\mathcal{I}^{*}$-Cauchy sequence, and then study their certain properties.

Article information

Source
Taiwanese J. Math., Volume 11, Number 2 (2007), 569-576.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500404709

Digital Object Identifier
doi:10.11650/twjm/1500404709

Mathematical Reviews number (MathSciNet)
MR2334006

Zentralblatt MATH identifier
1129.40001

Subjects
Primary: 40A05: Convergence and divergence of series and sequences
Secondary: 40A99: None of the above, but in this section 46A99: None of the above, but in this section

Keywords
statistical convergence statistical Cauchy sequence $\mathcal{I}$-convergence $\mathcal{I}$-Cauchy $\mathcal{I}^*$-Cauchy ideals of sets

Citation

Nabiev, Anar; Pehlivan, Serpil; Gürdal, Mehmet. ON $\mathcal{I}$-CAUCHY SEQUENCES. Taiwanese J. Math. 11 (2007), no. 2, 569--576. doi:10.11650/twjm/1500404709. https://projecteuclid.org/euclid.twjm/1500404709


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