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...

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Autores principales:	Sen,Mausumi, Haloi,Rupam, Tripathy,Binod Chandra
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2019
Materias:	Probabilistic normed space µ-statistical convergence µ-density convergence Point−wise and uniform convergence AP O condition
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000501039
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spelling	oai:scielo:S0716-091720190005010392020-01-07µ-Statistically convergent function sequences in probabilistic normed linear spacesSen,MausumiHaloi,RupamTripathy,Binod Chandra Probabilistic normed space µ-statistical convergence µ-density convergence Point−wise and uniform convergence AP O 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.38 n.5 20192019-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000501039en10.22199/issn.0717-6279-2019-05-0067
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Probabilistic normed space µ-statistical convergence µ-density convergence Point−wise and uniform convergence AP O condition
spellingShingle	Probabilistic normed space µ-statistical convergence µ-density convergence Point−wise and uniform convergence AP O condition Sen,Mausumi Haloi,Rupam Tripathy,Binod Chandra µ-Statistically convergent function sequences in probabilistic normed linear spaces
description	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	Sen,Mausumi Haloi,Rupam Tripathy,Binod Chandra
author_facet	Sen,Mausumi Haloi,Rupam Tripathy,Binod Chandra
author_sort	Sen,Mausumi
title	µ-Statistically convergent function sequences in probabilistic normed linear spaces
title_short	µ-Statistically convergent function sequences in probabilistic normed linear spaces
title_full	µ-Statistically convergent function sequences in probabilistic normed linear spaces
title_fullStr	µ-Statistically convergent function sequences in probabilistic normed linear spaces
title_full_unstemmed	µ-Statistically convergent function sequences in probabilistic normed linear spaces
title_sort	µ-statistically convergent function sequences in probabilistic normed linear spaces
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2019
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000501039
work_keys_str_mv	AT senmausumi μstatisticallyconvergentfunctionsequencesinprobabilisticnormedlinearspaces AT haloirupam μstatisticallyconvergentfunctionsequencesinprobabilisticnormedlinearspaces AT tripathybinodchandra μstatisticallyconvergentfunctionsequencesinprobabilisticnormedlinearspaces
_version_	1718439861384380416

µ-Statistically convergent function sequences in probabilistic normed linear spaces

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