a normed space $mathfrak{x}$ is said to have the fixed point property, if for each nonexpansive mapping $t : e longrightarrow e $ on a nonempty bounded closed convex subset $ e $ of $ mathfrak{x} $ has a fixed point. in this paper, we first show that if $ x $ is a locally compact hausdorff space then the following are equivalent: (i) $x$ is infinite set, (ii) $c_0(x)$ is infinite dimensional, (...

Katsaras 1 defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space. Some mathematicians have defined fuzzy norms on a vector space from various points of view 2–4 . In particular, Bag and Samanta 5 , following Cheng and Mordeson 6 , gave an idea of fuzzy norm in such a manner that the corresponding fuzzy metric is of Kramosil and Michálek type 7 . T...

In this paper, we have dealt with the concept of fuzzy b-closed and fuzzy bcompact set, and we study the characterization of fuzzy b-compact set by using fuzzy filterbases. We consider some relations between the fuzzy b-compact space and fuzzy b-closed space. Finally, the concept of bounded and semi bounded operators between fuzzy normed space are studied and some immediate results are also pro...

In this paper, a fuzzy version of the analytic form of Hahn-Banach extension theorem is given. As application, the Hahn-Banach theorem for rfuzzy bounded linear functionals on r-fuzzy normed linear spaces is obtained.

Wavelet analysis is a powerful tool withmodern applications as diverse as: image processing, signal processing, data compression, data mining, speech recognition, computer graphics, etc. The aim of this paper is to introduce the concept of atomic decomposition of fuzzy normed linear spaces, which play a key role in the development of fuzzy wavelet theory. Atomic decompositions appeared in appli...

In this paper, we obtain a characterization of linear spaces which may be normed so as to become complete, linear, normed metric spaces. In this connection, K. Kunugui and M. Fréchet have shown that every metric space S is isometric with a subset of a complete, linear, normed metric space. I t follows from our result that if the cardinal number of 5 is the limit of a denumerable sequence of car...

Let X be a normed space that satisfies the Johnson-Lindenstrauss lemma (J-L lemma, in short) in the sense that for any integer n and any x1, . . . , xn ∈ X there exists a linear mapping L : X → F, where F ⊆ X is a linear subspace of dimension O(log n), such that ‖xi − x j‖ ≤ ‖L(xi) − L(x j)‖ ≤ O(1) · ‖xi − x j‖ for all i, j ∈ {1, . . . , n}. We show that this implies that X is almost Euclidean ...