On the Mazur-Ulam problem in fuzzy anti-normed spaces
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2014-03-14 https://doi.org/10.14419/ijamr.v3i2.1936
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Abstract
The aim of this article is to proved a Mazur-Ulam type theorem in the strictly convex fuzzy anti-normed spaces.
Keywords: Fuzzy anti-normed space, Mazur-Ulam theorem, strictly convex.
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References
- C. Felbin, "Finite dimensional fuzzy normed linear spaces", Fuzzy Sets and Systems, Vol.48, No.2, (1992), pp.239-248.
- T. Bag, S.K. Samanta, "A comparative study of fuzzy norms on a linear space", Fuzzy Sets and Systems, Vol.159, No.6, (2008), 670-684.
- J.A. Baker, "Isometries in normed spaces", Amer. Math. Monthly, Vol.78, No.6, (1971), 655-658.
- S.C. Cheng, J.N. Mordeson, "Fuzzy linear operator and fuzzy normed linear spaces", Bull. Calcutta Math. Soc. Vol.86, (1994), 429-436.
- M. Eshaghi Gordji, N. Ghobadipour, "On the Mazur-Ulam theorem in fuzzy normed spaces", arXiv:0905.2166 (2009).
- Iqbal H. Jebril, T.K. Samanta, "Fuzzy anti-normed linear space", J. math. & Tech., February (2010), 66-77.
- D. Kangb,., H. Kohb, I. G. Choa, "On the Mazur-Ulam theorem in non-Archimedean fuzzy normed spaces", Appl. Math. Let. Vol.25, No.3, (2012), 301-304.
- S. Mazur, S. Ulam, "Sur les transformation isomtriques despaces vectoriels norms", C. R. Acad. Sci. Paris, Vol.194 (1932), 946-948.
- M. S. Moslehian and Gh. Sadeghi, "A Mazur-Ulam theorem in non-Archimedean normed spaces", Nonlinear Anal. Vol.69 (2008), 3405-3408.
- R. Saadati, S.M. Vaezpour, "Some results on fuzzy Banach spaces", J. Appl. Math. Computing, Vol.17, No. 1-2, (2005), 475-484.
- L.A. Zadeh, "Fuzzy sets", Inf. & Cont., Vol.8 (1965), 338-353.
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How to Cite
Abrishami-Moghaddam, M. (2014). On the Mazur-Ulam problem in fuzzy anti-normed spaces. International Journal of Applied Mathematical Research, 3(2), 93-96. https://doi.org/10.14419/ijamr.v3i2.1936Received date: 2014-02-05
Accepted date: 2014-03-01
Published date: 2014-03-14