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.

Downloads

Published

2009-07-30

Issue

Vol. 2 No. 2: (April 2009)

Section

Topology

License

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

On $\mathcal{I}$-convergence in the Topology Induced by Probabilistic Norms. (2009). European Journal of Pure and Applied Mathematics, 2(2), 195-212. https://www.ejpam.com/index.php/ejpam/article/view/77