EMIS ELibM Electronic Journals
Vol. 70, No. 2, pp. 97–109 (2018)

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

P. Malik, A. Ghosh and M. Maity

Department of Mathematics, The University of Burdwan, Golapbag, Burdwan-713104, West Bengal, India E-mail: pmjupm@yahoo.co.in and Department of Mathematics, The University of Burdwan, Golapbag, Burdwan-713104, West Bengal, India E-mail: buagbu@yahoo.co.in and Boral High School, Kolkata-700154, India E-mail: mepsilon@gmail.com

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.

Classification (MSC2000): 54E70; 40B05

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Electronic fulltext finalized on: 13 Mar 2018. This page was last modified: 25 Sep 2018.

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