On $oint$-convergence in the topology induced by probabilistic norms

Abstract

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