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

Vakeel A. Khan, Henna Altaf, Mohammad Faisal Khan

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.

Keywords


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

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References


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DOI: http://dx.doi.org/10.26713%2Fcma.v9i4.1197

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