On Generalized Difference Ideal Convergence in Generalized Probabilistic n-normed Spaces

  • Binod Chandra TripathyEmail author
  • Mausumi Sen
  • Soumitra Nath
Research Article


In this article, we introduce the concept of \(\varDelta ^{m}-I\)-convergent and \(\varDelta ^{m}-I\) Cauchy sequences in generalized probabilistic n-normed spaces and establish some results relating to this concept. We also study \(\varDelta ^{m}-I^{*}\) convergence in the same space. Statement Probabilistic norm generalizes and unifies different notions of norm, represented by a distance function, rather than a positive real number. Ideal convergence unifies many notions of convergence of sequences. In this article, we have introduced the notion of generalized difference ideal convergent sequences in probabilistic n-normed space, which generalizes and unifies many existing notions. Hence, the results of this article have been established in general setting.


Statistical metric Difference sequence space Ideal convergence Probabilistic norm 


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Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© The National Academy of Sciences, India 2019

Authors and Affiliations

  • Binod Chandra Tripathy
    • 1
    Email author
  • Mausumi Sen
    • 2
  • Soumitra Nath
    • 3
  1. 1.Department of MathematicsTripura UniversityAgartalaIndia
  2. 2.National Institute of Technology, SilcharSilcharIndia
  3. 3.Department of MathematicsSilchar PolytechnicSilcharIndia

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