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μ-Statistically Convergent Multiple Sequences in Probabilistic Normed Spaces

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Advances in Algebra and Analysis

Part of the book series: Trends in Mathematics ((TM))

Abstract

In this article, we introduce the notions of μ-statistically convergent and μ-statistically Cauchy multiple sequences in probabilistic normed spaces (in short PN-spaces). We also give a suitable characterization for μ-statistically convergent multiple sequences in PN-spaces. Moreover, we introduce the notion of μ-statistical limit points for multiple sequences in PN-spaces, and we give a relation between μ-statistical limit points and limit points of multiple sequences in PN-spaces.

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Acknowledgements

The work of the first author has been supported by the Research Project SB/S4/MS:887/14 of SERB - Department of Science and Technology, Govt. of India.

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Authors and Affiliations

  1. Department of Mathematics, NIT Silchar, Silchar, Assam, India

    Rupam Haloi & Mausumi Sen

Authors
  1. Rupam Haloi
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  2. Mausumi Sen
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Corresponding author

Correspondence to Mausumi Sen .

Editor information

Editors and Affiliations

  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India

    V. Madhu

  2. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India

    A. Manimaran

  3. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India

    D. Easwaramoorthy

  4. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India

    D. Kalpanapriya

  5. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India

    M. Mubashir Unnissa

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Haloi, R., Sen, M. (2018). μ-Statistically Convergent Multiple Sequences in Probabilistic Normed Spaces. In: Madhu, V., Manimaran, A., Easwaramoorthy, D., Kalpanapriya, D., Mubashir Unnissa, M. (eds) Advances in Algebra and Analysis. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-01120-8_40

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