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Published in:
2018 | OriginalPaper | Chapter
4. Fundamental Theorems in Fuzzy Normed Spaces
Authors : Yeol Je Cho, Themistocles M. Rassias, Reza Saadati
Published in: Fuzzy Operator Theory in Mathematical Analysis
Publisher: Springer International Publishing
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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.