Statistically pre-Cauchy sequences and bounded moduli

DOI: https://doi.org/10.12697/ACUTM.2003.07.01

Keywords: statistically convergent sequence, statistically pre-Cauchy sequence, modulus function

Let x=(x_k) be a sequence and let f be a bounded modulus. We prove that x is statistically pre-Cauchy if and only if

lim_n1/n²∑_j,k≤nf(|x_k−x_j|)=0.

This implies a theorem due to Connor, Fridy and Kline [4].

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Mehmet Gürdal, Suleyman Demirel University

Department of Mathematics