Strongly λ-statistically and strongly Valle-Poussin pre-Cauchy sequences in probabilistic metric spaces.

We introduce the notions of strongly λ-statistically pre-Cauchy and strongly Valle-Poussin pre-Cauchy sequences in probabilistic metric spaces endowed with strong topology. And we show that these two new notions are equivalent. Strongly λ-statistically convergent sequences are strongly λ-statistically pre-Cauchy sequences, and we give an example to show that there is a sequence in a probabilistic metric space which is strongly λ-statistically pre-Cauchy but not strongly λ-statistically convergent. [ABSTRACT FROM AUTHOR]