논문KCI 등재
On linear operators in Felbin's fuzzy normed linear space
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In this paper, we have obtained a few results on fuzzy boundedness of linear operators on Felbin's fuzzy normed linear spaces. The main result of this paper is an extension theorem for a strongly (weakly) fuzzy bounded linear operator. The existence of the inverse of a strongly (weakly) fuzzy bounded linear operator has also been established.
Abstract
In this paper, we have obtained a few results on fuzzy boundedness of linear operators on Felbin's fuzzy normed linear spaces. The main result of this paper is an extension theorem for a strongly (weakly) fuzzy bounded linear operator. The existence of the inverse of a strongly (weakly) fuzzy bounded linear operator has also been established.
참고문헌 (14)
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- C. Felbin, "Finite dimensional fuzzy normed linear spaces", Fuzzy Sets and Systems, 48, pp.239~248 (1992)
- C. Felbin, "Finite dimensional fuzzy normed linear spaces II", J. Analysis, 7, pp.117~131 (1999)
- P. Ji, "Completeness of fuzzy normed linear space of all weakly fuzzy bounded linear operators", Fuzzy Sets and Systems, 251, pp.92~100 (2014)
- O. Kaleva, "On fuzzy metric spaces", Fuzzy Sets and Systems, 12, pp.215~229 (1984)
- E. Kreyszig, "Introductory Functional Analysis with Applications" (2007), Wiley India
- M. Mizumoto, "Advances in Fuzzy Set Theroy and Applications", pp.153~164 (1979), North-Holland
- I. Sadeqi, "Fuzzy normed linear space and its topological structure", Chaos Solitons Fractals, 40, pp.2576~2589 (2009)
- M. Saheli, "Some properties of fuzzy norm of linear operators", Iran. J. Fuzzy Syst, 11(2), pp.121~139 (2014)
- M. Salehi, "Hahn Banach theorem on fuzzy ormed linear spaces", Ann. Fuzzy Math. Inform, 11(2), pp.293~300 (2016)
- J. Z. Xiao, "Fuzzy normed space of operators and its completeness", Fuzzy Sets and Systems, 133, pp.389~399 (2003)
- J. Z. Xiao, "Some basic theorems for linear operators between fuzzy normed spaces", J. Univ. Sci. Technol. China, 34(4), pp.414~430 (2004)
- J. Z. Xiao, "On linearly topological structure and property of fuzzy normed linear space", Fuzzy Sets and Systems, 125, pp.153~161 (2002)
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