Fuzzy barrels on locally convex fuzzy topological vector spaces

Daraby, Bayaz; Khosravi, N.; Rahimi, Asghar

doi:10.18514/mmn.2020.3197

Cited by 1 publication

(1 citation statement)

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“…Induced norms of these spaces may have very important applications in quantum particle physics for more details; see 21,22 . In recent past lots (more advanced reader), numerous references to the application of these spaces have been done in this direction on fuzzy functional analysis [23][24][25][26] . Structurally, the paper comprises the following: after this introductory section, In Section 2 gives basic definitions and preliminary results which are used in the sequel.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Real Pre-Hilbert Space and Some of Their Properties

Mohammedali

2022

Baghdad Sci.J

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In this work, two different structures are proposed which is fuzzy real normed space (FRNS) and fuzzy real Pre-Hilbert space (FRPHS). The basic concept of fuzzy norm on a real linear space is first presented to construct ( ,̃, ) space, which is a FRNS with some modification of the definition introduced by G. Rano and T. Bag. The structure of fuzzy real Pre-Hilbert space (FRPHS) is then presented which is based on the structure of FRNS. Then, some of the properties and related concepts for the suggested space FRN such as -neighborhood, closure of the set named ( ), the necessary condition for separable, fuzzy linear manifold (FLM) are discussed. The definition for a fuzzy seminorm on / is also introduced with the prove that a fuzzy seminorm on / is FRNS. The relationship between the ̆convergent sequence, ̆-Cauchy sequence and ̆completeness is then investigated in this work. The structure of FRPHS with some important properties concerning on this space are introduced and proved. In addition, the property of orthogonality with some important properties for these spaces is included, for example the annihilator of the set . The relation between FRPHS and FRNS is investigated in the present work. Finally, after introducing the structure of FRPHS, it leads naturally to the definition of the most important class of FRPHS, namely the fuzzy real Hilbert space (FRHS).

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Section: Introductionmentioning

confidence: 99%

Fuzzy Real Pre-Hilbert Space and Some of Their Properties

Mohammedali

2022

Baghdad Sci.J

View full text Add to dashboard Cite

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Fuzzy barrels on locally convex fuzzy topological vector spaces

Cited by 1 publication

References 12 publications

Fuzzy Real Pre-Hilbert Space and Some of Their Properties

Fuzzy Real Pre-Hilbert Space and Some of Their Properties

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