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

P. Malik; A. Ghosh; M. Maity

Authors

P. Malik Department of Mathematics, The University of Burdwan, Golapbag, Burdwan-713104, West Bengal, India Author
A. Ghosh Department of Mathematics, The University of Burdwan, Golapbag, Burdwan-713104, West Bengal, India Author
M. Maity Boral High School, Kolkata-700154, India Author

Keywords:

Probabilistic metric space, strong

I

-statistical convergence, strong

I

-statistical pre-Cauchy condition, strong

I^{*}

-statistical pre-Cauchy condition

Subjects:

54E70, 40B05

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.

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

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Strongly I and I∗-statistically pre-Cauchy double sequences in probabilistic metric spaces

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