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On the metrization problem of \(\nu \)-generalized metric spaces

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this paper we construct a counter-example to give a negative answer to Suzuki et al. (Open Math 13(1):510–517, 2015, Problem 5.1) on the metrization of \(\nu \)-generalized metric spaces. We also prove a sufficient condition for a \(\nu \)-generalized metric space with \(\nu \ge 4\) having a metric with the same convergence of sequences.

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Acknowledgements

The authors sincerely thank anonymous referees for several helpful comments. The authors also thank members of The Dong Thap Group of Mathematical Analysis and its Applications for their discussions on the manuscript.

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Authors and Affiliations

  1. Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Nguyen Van Dung

  2. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Nguyen Van Dung

  3. Faculty of Mathematics and Information Technology Teacher Education, Dong Thap University, Cao Lanh City, Dong Thap Province, Vietnam

    Vo Thi Le Hang

  4. Journal of Science, Dong Thap University, Cao Lanh City, Dong Thap Province, Vietnam

    Vo Thi Le Hang

Authors
  1. Nguyen Van Dung
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  2. Vo Thi Le Hang
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Correspondence to Nguyen Van Dung.

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Van Dung, N., Le Hang, V.T. On the metrization problem of \(\nu \)-generalized metric spaces. RACSAM 112, 1295–1303 (2018). https://doi.org/10.1007/s13398-017-0425-4

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  • DOI: https://doi.org/10.1007/s13398-017-0425-4

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