On the Mazur-Ulam problem in fuzzy anti-normed spaces

  • Authors

    • Majid Abrishami-Moghaddam Islamic Azad University, Birjand Branch, Iran.
    2014-03-14
    https://doi.org/10.14419/ijamr.v3i2.1936

  • 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.

  • References

    1. C. Felbin, "Finite dimensional fuzzy normed linear spaces", Fuzzy Sets and Systems, Vol.48, No.2, (1992), pp.239-248.
    2. 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.
    3. J.A. Baker, "Isometries in normed spaces", Amer. Math. Monthly, Vol.78, No.6, (1971), 655-658.
    4. S.C. Cheng, J.N. Mordeson, "Fuzzy linear operator and fuzzy normed linear spaces", Bull. Calcutta Math. Soc. Vol.86, (1994), 429-436.
    5. M. Eshaghi Gordji, N. Ghobadipour, "On the Mazur-Ulam theorem in fuzzy normed spaces", arXiv:0905.2166 (2009).
    6. Iqbal H. Jebril, T.K. Samanta, "Fuzzy anti-normed linear space", J. math. & Tech., February (2010), 66-77.
    7. 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.
    8. S. Mazur, S. Ulam, "Sur les transformation isomtriques despaces vectoriels norms", C. R. Acad. Sci. Paris, Vol.194 (1932), 946-948.
    9. M. S. Moslehian and Gh. Sadeghi, "A Mazur-Ulam theorem in non-Archimedean normed spaces", Nonlinear Anal. Vol.69 (2008), 3405-3408.
    10. R. Saadati, S.M. Vaezpour, "Some results on fuzzy Banach spaces", J. Appl. Math. Computing, Vol.17, No. 1-2, (2005), 475-484.
    11. 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.v3i2.1936

    Received date: 2014-02-05

    Accepted date: 2014-03-01

    Published date: 2014-03-14