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

Authors

  • Mohd Rafi Segi Rahmat The University of Nottingham Malaysia Campus
  • Harikrishnan Kanthen

Keywords:

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

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.

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How to Cite

Segi Rahmat, M. R., & Kanthen, H. (2009). On $\mathcal{I}$-convergence in the Topology Induced by Probabilistic Norms. European Journal of Pure and Applied Mathematics, 2(2), 195–212. Retrieved from https://ejpam.com/index.php/ejpam/article/view/77