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Fuzzy Normed Spaces and Fuzzy Metric Spaces

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Abstract

In this chapter, we define fuzzy normed spaces and show that every fuzzy normed space induces a fuzzy metric space. Then we consider the topology induced by fuzzy normed (metric) spaces and show some important topological properties of them. Next, we study fuzzy inner product spaces and some properties of these spaces.

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Author information

Authors and Affiliations

  1. Department of Mathematical Education, Gyeongsang National University, Jinju, Korea (Republic of)

    Yeol Je Cho

  2. School of Mathematical Science, University of Electronic Science and Technology of China, Chengdu, Sichuan, China

    Yeol Je Cho

  3. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  4. Department of Mathematics, Iran University of Science and Technology, Tehran, Iran

    Reza Saadati

Authors
  1. Yeol Je Cho
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  2. Themistocles M. Rassias
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  3. Reza Saadati
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Cho, Y.J., Rassias, T.M., Saadati, R. (2018). Fuzzy Normed Spaces and Fuzzy Metric Spaces. In: Fuzzy Operator Theory in Mathematical Analysis. Springer, Cham. https://doi.org/10.1007/978-3-319-93501-0_2

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