Bounded and Semi Bounded Inverse Theorems in Fuzzy Normed Spaces

Hamid Reza Moradi
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Hamid Reza Moradi: Islamic Azad University, Mashhad, Iran

International Journal of Fuzzy System Applications (IJFSA), 2015, vol. 4, issue 2, 47-55

Abstract: In this paper, the author introduces the notion of the complete fuzzy norm on a linear space. And the author considers some relations between the fuzzy completeness and ordinary completeness on a linear space, moreover a new form of fuzzy compact spaces, namely b-compact spaces, b-closed space is introduced. Some characterization of their properties is obtained. Also some basic properties for linear operators between fuzzy normed spaces are further studied. The notions of fuzzy vector spaces and fuzzy topological vector spaces were introduced in Katsaras and Liu (1977). These ideas were modified by Katsaras (1981), and in (1984) Katsaras defined the fuzzy norm on a vector space. In (1991) Krishna and Sarma discussed the generation of a fuzzy vector topology from an ordinary vector topology on vector spaces. Also Krishna and Sarma (1992) observed the convergence of sequence of fuzzy points. Rhie et al. (1997) Introduced the notion of fuzzy a-Cauchy sequence of fuzzy points and fuzzy completeness.

Date: 2015
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