t-BEST APPROXIMATION IN FUZZY NORMED SPACES

Document Type : Research Paper

Authors

1 Department of Mathematics, Amirkabir University, Tehran, Iran

2 Department of Mathematics, University of Yazd, Yazd, Iran

Abstract

The main purpose of this paper is to find t-best approximations in fuzzy normed spaces. We introduce the notions of t-proximinal sets and F-approximations and prove some interesting theorems. In particular, we investigate the set of all t-best approximations to an element from a set.

Keywords


[1] T. Bag and S. K. Samanta,Finite dimentional fuzzy normed linear spaces, J. Fuzzy Math.,
11(3)(2003), 678-705.
[2] S. C. Cheng and J. N. Mordeson,Fuzzy linear operator and fuzzy normed linear spaces, Bull.
Calcutta Math. Soc.,86 (1994), 429-436.
[3] F. Deutsch,Best approximation in inner product spaces, Springer-Verlag, 2001.
[4] A. George and P. Veeramani,On some results in fuzzy metric spaces, Fuzzy Sets and Systems,
64(1994), 395-399.
[5] A. George and P. Veeramani,On Some results of analysis for fuzzy metric spaces, Fuzzy Sets
and Systems,90 (1997), 365-368.
[6] R. Saadati and S. M. Vaezpour,Some results on fuzzy Banach spaces, J. Appl. Math. &
Computing,17(1-2) (2005), 475-484.
[7] I. Singer,Best approximation in normed linear spaces by elements of linear subspaces,
Springer-Verlag, 1970.
[8] P. Veeramani,Best approximation in fuzzy metric spaces, J. Fuzzy Math., 9(1) (2001), 75-80.
[9] L. A. Zadeh,Fuzzy sets, Inform. and Control, 8 (1965), 338-353.