µ-Statistically convergent function sequences in probabilistic normed linear spaces

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2019-05-0067

Keywords:

Probabilistic normed space, µ-statistical convergence, µ-density convergence, Point−wise and uniform convergence AP 0 condition

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.

Author Biographies

Mausumi Sen, National Institute of Technology.

Department of Mathematics.

Rupam Haloi, National Institute of Technology.

Department of Mathematics.

Binod Chandra Tripathy, Tripura University.

Department of Mathematics.

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Published

2019-12-17

How to Cite

[1]
M. Sen, R. Haloi, and B. C. . Tripathy, “µ-Statistically convergent function sequences in probabilistic normed linear spaces”, Proyecciones (Antofagasta, On line), vol. 38, no. 5, pp. 1039-1056, Dec. 2019.

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