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

  • Binod Chandra TripathyEmail author
  • Mausumi Sen
  • Soumitra Nath
Research Article
First Online:
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Abstract

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.

Keywords

Statistical metric Difference sequence space Ideal convergence Probabilistic norm 
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Notes

Compliance with ethical standards

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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