µ-Statistically convergent function sequences in probabilistic normed linear spaces

Abstract

In this article, we introduce the concept of µ-statistical convergence and µ-density convergence of sequences of functions defined on a compact subset D of the probabilistic normed space (X, N, ∗), where µ is a finitely additive two valued measure. In particular, we introduce the notions of µ-statistical uniform convergence as well as µ-statistical point-wise convergence of sequences of functions in probabilistic normed space (in short PN-space) and we give some characterization results on these two convergences of sequences of functions in PN-space. We have also observed that µ-statistical uniform convergence of sequences of functions in PN-spaces inherits the basic properties of uniform convergence.