Abstract

In this paper we consider the notion of strongly $I$-statistically pre-Cauchy double sequences in probabilistic metric spaces in line of Das et.\ al.\ (\emph{On $I$-statistically pre-Cauchy sequences}, Taiwanese J. Math 18 (1) (2014), 115--126) and introduce the new concept of strongly $I^*$-statistically pre-Cauchy double sequences in probabilistic metric spaces. We mainly study interrelationship among strong $I$-statistical convergence, strong $I$-statistical pre-Cauchy condition and strong $I^*$-statistical pre-Cauchy condition for double sequences in probabilistic metric spaces and examine some basic properties of these notions.

Keywords: Probabilistic metric space; strong $I$-statistical convergence; strong $I$-statistical pre-Cauchy condition; strong $I^*$-statistical pre-Cauchy condition.

MSC: 54E70, 40B05

Pages:  97$-$109     

Volume  70 ,  Issue  2 ,  2018