Ideal convergent sequences of functions in probabilistic normed spaces

Volume 26, Issue 3, pp 249--254 http://dx.doi.org/10.22436/jmcs.026.03.04

Publication Date: November 09, 2021 Submission Date: September 13, 2021 Revision Date: September 27, 2021 Accteptance Date: October 07, 2021

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Authors

V. A. Khan - Department of Mathematics , Aligarh Muslim University, Aligarh-202002, India. H. Altaf - PG Department of Mathematics, Government Degree College, Baramulla-193101, India. M. Alam - Department of Mathematics and IT Center for Preparatory Studies , Sultan Qaboos University, P.O. Box 162-PC, 123 Al Khoud, Muscat, Sultanate of Oman.

Abstract

In the present article, we have defined the notion of \(I\)-pointwise convergence and \(I\)-uniform convergence of sequence of functions defined on a probabilistic normed space with respect to the probabilistic norm \(\nu\). Further we have given the Cauchy criteria for \(I\)-pointwise and \(I\)-uniform convergence in PNS. Also, we have proved certain results on continuity of functions with respect to \(\nu\) in PNS.

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Keywords

• Ideal
• filter
• probabilistic normed spaces
• sequence of functions

MSC

•  40A35
•  46S50

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