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

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.