A comparative study of fuzzy norms on a linear space

Bag, T.; Samanta, Sourav

doi:10.1016/j.fss.2007.09.011

Cited by 38 publications

(27 citation statements)

References 7 publications

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“…Samanta [2] introduced a new concept of fuzzy norm, and studied the properties of finite dimensional fuzzy normed linear spaces. A comparative study on fuzzy norms introduced Katsaras, Felbin and Bag and Samanta was made in paper [4]. Other approaches for fuzzy normed linear spaces can be found in [1,7,10,44,48,51,60].…”

Section: Fuzzy Normed Linear Spacesmentioning

confidence: 99%

The Fuzzification of Classical Structures: A General View

Dzițac

2015

INT J COMPUT COMMUN

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Section: Fuzzy Normed Linear Spacesmentioning

confidence: 99%

The Fuzzification of Classical Structures: A General View

Dzițac

2015

INT J COMPUT COMMUN

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“…It follows that N (x, t + ) ≥ α. (4) and (6) follow from (1) while (5) follows from (1) and (4). For N 1 , N 2 fuzzy seminorms on E, the following are equivalent.…”

Section: Fuzzy Seminorms Fuzzy Normsmentioning

confidence: 99%

“…The converse follows in an analogous way. (4) Assume that x ∈ A o . Since A o is the complement of the closure A c of A c = E \ A, we have that x / ∈ A c .…”

Section: Ifmentioning

confidence: 99%

Locally Convex Topologies Induced by Fuzzy Norms

Katsaras

2013

Global Journal of Mathematical Analysis

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It is shown that a Hausdorff topological vector space E is fuzzy normable iff its topology is a metrizable locally convex topology. Subspaces, product and quotient spaces of fuzzy normed spaces are investigated. Also the notion of the tensor product of two fuzzy normed norms is introduced and it is proved that the induced locally convex topology coincides with the projective tensor product topology.

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“…In the paper [4], Bag and Samanta introduced different types of continuities and boundedness for linear operators and established the principles of fuzzy functional analysis. A comparative study on fuzzy norms introduced by Katsaras, by Felbin and by Bag and Samanta was made in paper [5]. A new concept of fuzzy normed space was introduced by Saadati and Vaezpour in [15].…”

Section: Introductionmentioning

confidence: 99%