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

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.