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Fuzzy Normed Spaces and Fuzzy Metric Spaces

In: Fuzzy Operator Theory in Mathematical Analysis

Author

Listed:
  • Yeol Je Cho

    (Gyeongsang National University, Department of Mathematical Education
    University of Electronic Science and Technology of China, School of Mathematical Science)

  • Themistocles M. Rassias

    (National Technical University of Athens, Department of Mathematics)

  • Reza Saadati

    (Iran University of Science and Technology, Department of Mathematics)

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.

Suggested Citation

  • Yeol Je Cho & Themistocles M. Rassias & Reza Saadati, 2018. "Fuzzy Normed Spaces and Fuzzy Metric Spaces," Springer Books, in: Fuzzy Operator Theory in Mathematical Analysis, chapter 0, pages 11-43, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-93501-0_2
    DOI: 10.1007/978-3-319-93501-0_2
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