FUZZY REFLEXIVITY OF FELBIN'S TYPE FUZZY NORMED LINEAR SPACES AND FIXED POINT THEOREMS IN SUCH SPACES

Document Type: Research Paper

Authors

1 Department of Mathematics, Visva-Bharati, Santiniketan-731235, West Ben- gal, India

2 Department of Mathematics, Visva-Bharati, Santiniketan-731235, West Bengal, India

Abstract

An idea of fuzzy reexivity of Felbin's type fuzzy normed linear
spaces is introduced and its properties are studied. Concept of fuzzy uniform
normal structure is given and using the geometric properties of this concept
xed point theorems are proved in fuzzy normed linear spaces.

Keywords


bibitem{1}
 T.Bag, S.K.Samanta, Finite dimensional fuzzy normed linear spaces, The Journal of Fuzzy Mathematics,
{bf 11}textbf{(3)}(2003), 687-705.

bibitem{2}
 T.Bag, S.K.Samanta, Fuzzy bounded linear operators, Fuzzy Sets and Systems,
{bf 151}(2005), 513-547.

bibitem{3}
 T.Bag, S.K.Samanta, Fixed point theorems in fuzzy normed linear spaces, Information Sciences, Vol. 176 (2006) 2910-2931.
{bf 176}(2006), 2910-2931.

bibitem{4}
[4] T.Bag, S.K.Samanta, Fixed point theorems in Felbin's type fuzzy normed linear spaces,\ The Journal of Fuzzy Mathematics, Vol. 16, No. 1 (2008) 243-260.
{bf 16}textbf{(1)}(2008), 243-260.

bibitem{5}
 T.Bag, S.K.Samanta, A comparative study of fuzzy norms on a linear space, Fuzzy Sets and Systems, Vol. 159 (2008) 670-684.
{bf 159}(2008), 670-684.

bibitem{6}
T.Bag, S.K.Samanta, Fuzzy bounded linear operators in Felbin's type fuzzy normed linear spaces, Fuzzy Sets and Systems, Vol. 159 (2008) 685-707.
{bf 159}(2008), 685-707.

bibitem{7}
 T.Bag, S.K.Samanta, Fuzzy reflexive spaces, The Journal of Fuzzy Mathematics ( accepted for publication ).

bibitem{8}
S.C.Cheng, J.N.Mordeson, Fuzzy linear operators and fuzzy normed linear spaces,\ Bull.Cal.Math.Soc. Vol. 86 (1994) 429-436.
{bf 86}(1994), 429-436.

bibitem{9}
 D.Dubois, H.Prade, Fuzzy elements in a fuzzy set, Proc. 10th Inter. Fuzzy Systems Assoc. ( IFSA ) Congress, Beijing, Springer, 2005, 55-60.

bibitem{10}
C.Felbin, Finite dimensional fuzzy normed linear spaces, Fuzzy Sets and Systems,
 {bf 48}(1992) 239-248.

bibitem{11}
C.Felbin, Finite dimensional fuzzy normed linear spaces II, J.Analysis,
{bf 7}(1999) 117-131.

bibitem{12}
A. Hasankhani, A. Nazari, M. Saheli, Some properties of fuzzy Hilbert spaces and norm of operators, Iranian Journal of Fuzzy Systems,
{bf 7}textbf{(3)}(2010), 129-157.

bibitem{13}
O.Kaleva, S.Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems,
{bf 12}(1984) 215-229.

bibitem{14}
 A.K.Katsaras, Fuzzy topological vector spaces, Fuzzy Sets and Systems,
{bf 12}(1984) 143-154.

bibitem{15}
 W.A.Kirk, A fixed point theorem for mappings which do not increase distances, Am. Math. Monthly {bf 72}(1965) 1004-1006.

bibitem{16}
A.K.Kramosil, J.Michalek, Fuzzy metric and statistical metric spaces, Kybernetica
{bf 11}(1975) 326-334.

bibitem{17}
 M.Mizumoto, J.Tanaka, Some properties of fuzzy numbers in : M.M.Gupta et al. Editors, Advances in Fuzzy Set Theory and Applications ( North-Holland, New-York, 1979 ) 153-164.

bibitem{18}
[18] A. Narayanan, S. Vijyabalaji, Thillaigovindan, Intuitionistic fuzzy bounded linear operators, Iranian Journal of Fuzzy Systems,
{bf 4}textbf{(1)}(2007), 89-101.