Some properties of sequences in gradual normed spaces

Ettefagh, Mina; Etemad, Sina; Azari, Farnaz Y.

doi:10.1142/s1793557120500850

“…They studied various properties of the space from both the algebraic and topological point of view. Further progress in this direction has been occurred due to Ettefagh, Azari, and Etemad (see [6], [7]) and many others. For extensive study on gradual real numbers one may refer to ( [1], [4], [18], [27]).…”

Section: Introductionmentioning

confidence: 98%

“…Research on the convergence of sequences in gradual normed linear spaces has not yet gained much ground and it is still in its infant stage. The research carried out so far shows a strong analogy in the behavior of convergence of sequences in gradual normed linear spaces (for details one may refer to [6], [7], [23]).…”

Section: Introductionmentioning

confidence: 99%

On lacunary statistical convergence of sequences in gradual normed linear spaces

Choudhury¹,

Debnath²

2022

AMI

6

0

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“…They studied various properties of the space from both the algebraic and topological point of view. Further progress in this direction has been occurred due to Ettefagh, Azari, and Etemad (see [6], [7]) and many others. For extensive study on gradual real numbers one may refer to ( [1], [5][12], [18], [21], [22]).…”

Section: Introductionmentioning

confidence: 98%

“…Research on the convergence of sequences in gradual normed linear spaces has not yet gained much ground and it is still in its infant stage. The research carried out so far shows a strong analogy in the behavior of convergence of sequences in gradual normed linear spaces (for details one may refer to [6], [7], [15]).…”

Section: Introductionmentioning

confidence: 99%

On I- Convergence of Sequences in Gradual Normed Linear Spaces

Choudhury

¹

,

Debnath

²

2021

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In this paper, we introduce the concepts of $\mathcal{I}$ and $\mathcal{I^{*}}-$convergence of sequences in gradual normed linear spaces. We study some basic properties and implication relations of the newly defined convergence concepts. Also, we introduce the notions of $\mathcal{I}$ and $\mathcal{I^{*}}-$Cauchy sequences in the gradual normed linear space and investigate the relations between them.

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“…Recently, Sadeqi and Azari [9] have studied some properties of gradual numbers and introduced gradual normed linear space. In [4], Ettefagh et al investigated some properties of sequences in gradual normed spaces.…”

Section: Introductionmentioning

confidence: 99%

On Some Topological Properties in Gradual Normed Spaces

Ettefagh¹,

Azari²,

Etemad³

2020

Self Cite

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In this paper, we have investigated some topological properties of sets in a given gradual normed space. We have stated gradual Hausdorff property and then,we have studied the relationship between gradual closed sets and gradual compact sets. Also, we have given a result about having the closure point for an innite set in a gradual normed space. In the end, we have provided some illustrative examples.

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Some properties of sequences in gradual normed spaces

Cited by 11 publications

References 6 publications

On lacunary statistical convergence of sequences in gradual normed linear spaces

On lacunary statistical convergence of sequences in gradual normed linear spaces

On I- Convergence of Sequences in Gradual Normed Linear Spaces

On Some Topological Properties in Gradual Normed Spaces

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