A New Type of Ideal Convergence of Difference Sequence in Probabilistic Normed Space

Authors

  • Vakeel A. Khan Department of Mathematics, Aligarh Muslim University, Aligarh 202002
  • Henna Altaf Department of Mathematics, Aligarh Muslim University, Aligarh 202002
  • Mohammad Faisal Khan College of Science and Theoretical Studies,Saudi Electronic University, Riyadh 11673

DOI:

https://doi.org/10.26713/cma.v9i4.1197

Keywords:

Triangular norm, Probabilistic normed space, \(\Delta I\)-convergence, \(\Delta I^{*}\)-convergence, \(\Delta I\)-limit points, \(\Delta I\)-cluster points

Abstract

The idea of difference sequence sets \(X(\Delta)=\{x=(x_{k}):\Delta x\in X\}\) with \(X=l_{\infty}\), \(c\) and \(c_{0}\) was introduced by Kizmaz [10]. Mursaleen and Mohiuddine [13] defined the idea of probabilistic normed space(PNS) and the ideal convergence in PNS. Motivated by the above two concepts, we in this paper introduce the notion of   difference \(I\)-convergent  sequence  in PNS and study the elementary properties of this convergence.

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References

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Published

30-12-2018
CITATION

How to Cite

Khan, V. A., Altaf, H., & Khan, M. F. (2018). A New Type of Ideal Convergence of Difference Sequence in Probabilistic Normed Space. Communications in Mathematics and Applications, 9(4), 737–745. https://doi.org/10.26713/cma.v9i4.1197

Issue

Vol. 9 No. 4 (2018)

Section

Research Article

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