Strongly $I$ and $I^*$-statistically pre-Cauchy double sequences in probabilistic metric spaces

Abstract

In this paper we consider the notion of strongly $I$-statisticallypre-Cauchy double sequences in probabilistic metric spaces in lineof Das et.\ al.\ (\emph{On $I$-statistically pre-Cauchysequences}, Taiwanese J. Math 18 (1) (2014), 115–126) andintroduce the new concept of strongly $I^*$-statisticallypre-Cauchy double sequences in probabilistic metric spaces. Wemainly study interrelationship among strong $I$-statisticalconvergence, strong $I$-statistical pre-Cauchy condition andstrong $I^*$-statistical pre-Cauchy condition for double sequencesin probabilistic metric spaces and examine some basic propertiesof these notions.