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On rough convergence of ρ-Cauchy sequence of triple sequences
Analysis (Germany), 2019AbstractIn this paper we define and study rough convergence of triple sequences and the set of rough limit points of a triple sequence. We also investigate the relations between the set of cluster points and the set of rough limit points of Cauchy sequences of triple sequence spaces.
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(2010). Quasi-Cauchy Sequences. The American Mathematical Monthly: Vol. 117, No. 4, pp. 328-333.
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STATISTICALLY PRE-CAUCHY SEQUENCES
Analysis, 1994Summary: A sequence \(x = \langle x_ k \rangle\) is statistically pre-Cauchy if \[ \lim_ n n^{-2} \biggl | \bigl \{ (j,k) : | x_ k - x_ j | \geq \varepsilon\;j,k \leq n \bigr \} \biggr | = 0 \] for every \(\varepsilon>0\). Statistically convergent sequences are statistically pre-Cauchy and any bounded statistically pre-Cauchy sequence with a nowhere ...
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