Fuzzy Farthest Points and Fuzzy Best Approximation Points in Fuzzy Normed Spaces

Subject Areas : Applied Mathematics

Hamid  Mazaheri Tehrani ¹ (Faculty of Mathematics, Yazd University, Yazd, Iran)
S. M  Mouavi Shams Abad ² (Faculty of Mathematics, Vali-e-asr University of Rafsenjan, Rafsenjan, Iran)
M. A  Dehghan ³ (Faculty of Mathematics, Vali-e-asr University of Rafsenjan, Rafsenjan, Iran)
Z.  Bizhanzadeh ⁴ (Faculty of Mathematics, Yazd University, Yazd, Iran)

Received: 2018-06-14 Accepted : 2019-02-23 Published : 2019-05-01

Keywords: Fuzzy farthest orthogonality, Fuzzy farthest points, Fuzzy best approximation points, Normed fuzzy space,

Abstract :

In this paper we define fuzzy farthest points, fuzzy best approximation points and farthest orthogonality in fuzzy normed spaces and we will find some results. We prove some existence theorems, also we consider fuzzy Hilbert and show every nonempty closed and convex subset of a fuzzy Hilbert space has an unique fuzzy best approximation.It is well know that the conception of fuzzy sets, firstly defined by Zadeh in 1965. Fuzzy set theory provides us with a framework which is wider than that of classical set theory. Various mathematical structures, whose features emphasize the effects of ordered structure, can be developed on the theory. The theory of fuzzy sets has become an area of active research for the last forty years. On the other hand, the notion of fuzzyness has a wide application in many areas of science and engineering, chaos control, nonlinear dynamical systems, etc. In physics, for example, the fuzzy structure of space time is followed by the fat that in strong quantum gravity regime space time points are determined in a fuzzy manner.

References:

[1]T. Bag and S.K. Samanta. Finite dimensional fuzzy normed linear spaces.
J. Fuzzy Math., 2003, 11(3), 687-705.

[2]T. Bag and S.K. Samanta. xed point theorems on fuzzy normed linear
spaces. Inform. Sci., 2003, 176, 2910-2931.

[3]T. Bag and S.K. Samanta. Some xed point theorems in fuzzy normed
linear spaces. Inform. Sci., 2007, 177, 3271-3289.

[4]A. George and P. Veeramani. On some results in fuzzy metric spaces.
Fuzzy Sets and Systems, 1994, 64(3), 395-399.
30

[5]M. Goudarzi and S. M. Vaezpour. On the denition of fuzzy Hilbert
spaces and its application The Journal of Nonlinear Science and
Applications, J. Nonlinear Sci. Appl., 2009, 2, 46-59.

[6]M. A. Moghadam. Best proximity pairs in fuzzy metric spaces. Journal
of Applied Sciences, 2012, 3, 1-4.

[7]S. A. M. Mohsen Hosseini, H. Mazaheri, and M. A. Dehghan.
Approximate xed point in fuzzy normed spaces for nonlinear maps.
Iranian Journal of Fuzzy System, 2013, 10(1), 135-142.

[8]R. Vasuki and P. Veeramani. Fixed point theorems and Cauchy sequences
in fuzzy metric spaces. Fuzzy Sets and Systems, 2003, 135(3), 415-417.

[9]S. M. Vaezpour and F. Karimi. t-best approximation in fuzzy normed
spaces. Iran. J. Fuzzy Syst., 2008, 5(2), 93-99.