ON FELBIN’S-TYPE FUZZY NORMED LINEAR SPACES AND FUZZY BOUNDED OPERATORS
نویسندگان
1 Department of Mathematics, Semnan University, Semnan, Iran
2 Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
3 Department of Mathematics, Sabzevar Tarbiat Moallem University, Sabzevar, Iran
doi
10.22111/ijfs.2011.301چکیده
In this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the Bag and Samanta’s operator norm on Felbin’s-type fuzzy normed spaces. In particular, the completeness of this space is studied. By some counterexamples, it is shown that the inverse mapping theorem and the Banach-Steinhaus’s theorem, are not valid for this fuzzy setting. Also finite dimensional normed fuzzy spaces are considered briefly. Next, a Hahn-Banach theorem for weakly fuzzy bounded linear functional with some of its applications are established.
