On $\mathcal{I}$-convergence in the Topology Induced by Probabilistic Norms

Mohd Rafi Segi Rahmat, Harikrishnan Kanthen

Abstract

The concepts of $\mathcal{I}$ -convergence is a natural generalization of statistical convergence and it is dependent on the notion of the ideal of subsets of $\mathbb{N}$ of positive integer set. In this paper we study the $\mathcal{I}$ -convergence of sequences, $\mathcal{I}$ -convergence of sequences of functions and $\mathcal{I}$-Cauchy sequences in probabilistic normed spaces and prove some important results.

Keywords

probabilistic norm; ideal convergence; statistical convergence; ideal Cauchy sequence; F-topology

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