## Statistically pre-Cauchy sequences and Orlicz functions.(English)Zbl 1150.40006

Summary: Let $$x= (x_i)$$ be a sequence and let $$M$$ be a bounded Orlicz function. We prove that $$x$$ is statistically pre-Cauchy if and only if $\lim_n\frac 1{n^2}\sum_{j, i\leq n} M ( \frac{|x_i-x_j|}{\rho})=0.$ This implies a theorem due to J. Connor, J. Fridy and J. Kline [Analysis 14, No.4, 311–317 (1994; Zbl 0810.40001)].

### MSC:

 40A30 Convergence and divergence of series and sequences of functions

Zbl 0810.40001