ON FELBIN’S-TYPE FUZZY NORMED LINEAR SPACES AND FUZZY BOUNDED OPERATORS

Document Type: Research Paper

Authors

1 Department of Mathematics, Sabzevar Tarbiat Moallem University, Sabzevar, Iran

2 Department of Mathematics, Semnan University, Semnan, Iran

3 Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

Abstract

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.

Keywords


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