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2011•Iranian journal of fuzzy systemsRequires access

GRADUAL NORMED LINEAR SPACE

Ildar Sadeqi, Farnaz Yaqub Azari

Open publisher page 11 citations

Abstract

In this paper, the gradual real numbers are considered and the notion of the gradual normed linear space is given. Also some topological properties of such spaces are studied, and it is shown that the gradual normed linear space is a locally convex space, in classical sense. So the results in locally convex spaces can be translated in gradual normed linear spaces. Finally, we give an example of a gradual normed linear space which is not normable in classical analysis.

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What this paper is about

In this paper, the gradual real numbers are considered and the notion of the gradual normed linear space is given. Also some topological properties of such spaces are studied, and it is shown that the gradual normed linear space is a locally convex space, in classical sense. So the results in locally convex spaces can be translated in gradual normed linear spaces. Finally, we give an example of a gradual normed linear space which is not normable in classical analysis.

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OpenAlex reports 11 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, the gradual real numbers are considered and the notion of the gradual normed linear space is given. Also some topological properties of such spaces are studied, and it is shown that the gradual normed linear space is a locally convex space, in classical sense. So the results in locally convex spaces can be translated in gradual normed linear spaces. Finally, we give an example of a gradual normed linear space which is not normable in classical analysis.

Key concepts: Normed vector space, Strictly convex space, Reflexive space, Mathematics, Space (punctuation), Continuous linear operator, Locally convex topological vector space, Functional analysis

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