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Fundamental Theorems in Fuzzy Normed Spaces

  • Yeol Je Cho
  • Themistocles M. Rassias
  • Reza Saadati
Chapter

Abstract

Some important theorems in this chapter are the open mapping theorem and the closed graph theorem. These are the cornerstones of the theory of fuzzy Banach spaces. Open mapping theorem states that a fuzzy bounded linear operator T from a fuzzy Banach space onto a fuzzy Banach space is an open mapping, that is, maps open sets onto open sets. Closed graph theorem gives conditions under which a closed linear operator is fuzzy bounded. Closed linear operators are of importance in physical and other applications.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Yeol Je Cho
    • 1
    • 2
  • Themistocles M. Rassias
    • 3
  • Reza Saadati
    • 4
  1. 1.Department of Mathematical EducationGyeongsang National UniversityJinjuKorea (Republic of)
  2. 2.School of Mathematical ScienceUniversity of Electronic Science and Technology of ChinaChengduChina
  3. 3.Department of MathematicsNational Technical University of AthensAthensGreece
  4. 4.Department of MathematicsIran University of Science and TechnologyTehranIran

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