in this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~the idea of equivalent quasi-norm families is introduced.~riesz lemma is established in this space.~finally,~we re-define b-s fuzzy norm and prove that it induces a generating space of quasi-norm family.

in the present paper, we rst modify the concepts of weakly fuzzy boundedness, strongly fuzzy boundedness, fuzzy continuity, strongly fuzzy continuity and weakly fuzzy continuity. then, we try to nd some relations by making a comparative study of the fuzzy norms of linear operators.

In the present paper, we investigate a connection between two fuzzy inner product one of which arises from Felbin's fuzzy norm and the other is based on Bag and Samanta's fuzzy norm. Also we show that, considering a fuzzy inner product space, how one can construct another kind of fuzzy inner product on this space.

the present paper introduces the notion of the complete fuzzy norm on a linear space. and, some relations between the fuzzy completeness and ordinary completeness on a linear space is considered, moreover a new form of fuzzy compact spaces, namely b-compact spaces and b-closed spaces are introduced. some characterizations of their properties are obtained.

Fuzzy best simultaneous approximation of a finite number of functions is considered. For this purpose, a fuzzy norm on $Cleft (X, Y right )$ and its fuzzy dual space and also the  set of subgradients of a fuzzy norm are introduced. Necessary case of a proved theorem about characterization of simultaneous approximation will be extended to the fuzzy case.

In the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. In particular, it isshown that the Cauchy-Schwarz inequality holds. Moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy Hilbert space has a complementary subspace.Finally, the notions of fuzzy bo...

in the present paper, we study some properties of fuzzy norm of linear operators. at first the bounded inverse theorem on fuzzy normed linear spaces is investigated. then, we prove hahn banach theorem, uniform boundedness theorem and closed graph theorem on fuzzy normed linear spaces. finally the set of all compact operators on these spaces is studied.

In this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~The idea of equivalent quasi-norm families is introduced.~Riesz lemma is established in this space.~Finally,~we re-define B-S fuzzy norm and prove that it induces a generating space of quasi-norm family.

in a fuzzy metric space (x;m; *), where * is a continuous t-norm,a locally fuzzy contraction mapping is de ned. it is proved that any locally fuzzy contraction mapping is a global fuzzy contractive. also, if f satis es the locally fuzzy contractivity condition then it satis es the global fuzzy contrac-tivity condition.