Statistically pre-Cauchy sequences and bounded moduli
Keywords:
statistically convergent sequence, statistically pre-Cauchy sequence, modulus function
Abstract
Let x=(xk) be a sequence and let f be a bounded modulus. We prove that x is statistically pre-Cauchy if and only if
limn 1/n2∑j,k≤nf(|xk−xj|)=0.
This implies a theorem due to Connor, Fridy and Kline [4].
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