Statistically pre-Cauchy double sequences.(English)Zbl 1265.40020

Summary: Let $$x=(x_{jk})$$ be a double sequence and $$M$$ be a bounded Orlicz function. We prove that $$x$$ is statistically pre-Cauchy if and only if $\lim\limits_{m, n}\frac{1}{m^2n^2}\sum_{j, p\leq m}\sum_{k, q\leq n} M\bigg(\frac{|x_{jk}-x_{pq}|}{\rho}\bigg)=0.$ The main purpose of this paper is to extend the results of V. A. Khan and Q. M. D. Lohani [Southeast Asian Bull. Math. 31, No. 6, 1107–1112 (2007; Zbl 1150.40006)] from single to double sequences.

MSC:

 40A35 Ideal and statistical convergence 40B05 Multiple sequences and series

Zbl 1150.40006