Research Article
On Fixed Point Theorem in Non-Archimedean Fuzzy Normed Spaces
- University of Ibadan, Ibadan
Abstract
Let (X, N) be a non-archimedean fuzzy normed space and (X, k.k), a non-archimedean normed space where X is a linear space over a linearly ordered non-archimedean field K with a non-archimedean valuation. We give a proof of the fixed point theorem in non-archimedean Fuzzy normed space.
How to Cite
M. E. Egwe, On Fixed Point Theorem in Non-Archimedean Fuzzy Normed Spaces, Int. J. Anal. Appl. 18 (2020), 99–103. https://doi.org/10.28924/2291-8639-18-2020-99
BibTeX
@article{Egwe2020,
author = {Egwe, M.E.},
title = {On Fixed Point Theorem in Non-Archimedean Fuzzy Normed Spaces},
journal = {Int. J. Anal. Appl.},
volume = {18},
year = {2020},
pages = {99--103},
doi = {10.28924/2291-8639-18-2020-99}
}References
- [1] D.Burago, Y.Burago, S.Ivanon: A course in Metric Geometry, Amer. Math. Soc. 2001.
- [2] Y.Je Cho, T.M. Rassias, R.Saadati: Fuzzy Operator Theory in Mathematical Analysis. Springer International Publishing, 2018
- [3] A. Granas, J. Dugunji: Fixed Point Theory, Springer, 2003.
- [4] D.Kangb, H. Kohb, I.G. Chao: On the Mazur-Ulam theorem in non-archimedean fuzzy normed spaces, Appl. Math. Lett. 25(2012), 301-304.
- [5] H. Mamghaderi, H.P. Masiha: On Stationary Points of Multivalued Strongly Contractive Mappings in Partially Ordered Ultrametric Spaces and non-Archimedean Normed Spaces. p-Adic Numbers, Ultr. Anal. Appl. 9(2)(2017), 144-150.
- [6] M.S. Moslehian, G. Sadeghi: A Mazur-Ulam theorem in non-archimedean normed spaces, Nonlinear Anal., Theory Methods Appl. 69(2008), 3405-3408.
- [7] A. Narayanan, S. Vijayabalaji: Fuzzy n-normed linear spaces. Int. J. Math. Math. Sci. 24(2005), 3963-3977.
- [8] C. Petalas, T. Vidalis: A fixed point theorem in non-archimedean vector spaces,Proc. Amer. Math. Soc. 118(3)(1993), 819-821.
- [9] A.C.M. Rooij: Non-Archimedean functional Analysis, Marcel Dekker NY, 1978.
- [10] F.Shi, C. Huang: Fuzzy bases and the fuzzy dimension of fuzzy vector spaces, Math. Commun. 15(2010), 303-310.
- [11] Z. Wang, P.K. Sahoo: Stability of an ACQ-functional equation in various Stability of an ACQ-functional equation in various. J. Nonlinear Sci. Appl. 8(2015), 64-85.