Existence of a class of vector-valued and multivariate α-fractal functions on a hype-rectangle of Rq.
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| Title: | Existence of a class of vector-valued and multivariate α-fractal functions on a hype-rectangle of Rq. |
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| Authors: | Verma, Shubham Kumar1 (AUTHOR) vrmshubham@gmail.com, Boulaaras, Salah2 (AUTHOR) s.boularas@qu.edu.sa, Guefaifia, Rafik2 (AUTHOR) r.guefaifia@qu.edu.sa |
| Source: | Fixed Point Theory & Algorithms for Sciences & Engineering. 4/14/2026, Vol. 2026 Issue 1, p1-12. 12p. |
| Subjects: | Vector valued functions, Fractal analysis, Approximation error, Weierstrass-Stone theorem, Continuous functions |
| Abstract: | In this article, we first prove the existence of a class of vector-valued and multivariate α-fractal functions on a hype-rectangle of R q . After that, we show that the set of functions with any possible fixed dimension in the continuous function space is dense with respect to uniform norm. Building on this, we also study dimension preserving approximation in this general setting. We then introduce and study some constrained approximation aspects based on dimension-preserving notion. Further, we prove some approximation theoretic results (such as Weierstrass approximation theorem) of the constructed vector-valued and multivariate α-fractal functions on a hype-rectangle of R q . In particular, we show the existence of a dense subset of α-fractal functions in the continuous functions space. [ABSTRACT FROM AUTHOR] |
| Copyright of Fixed Point Theory & Algorithms for Sciences & Engineering is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 193858977 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Existence of a class of vector-valued and multivariate α-fractal functions on a hype-rectangle of Rq. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Verma%2C+Shubham+Kumar%22">Verma, Shubham Kumar</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> vrmshubham@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Boulaaras%2C+Salah%22">Boulaaras, Salah</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> s.boularas@qu.edu.sa</i><br /><searchLink fieldCode="AR" term="%22Guefaifia%2C+Rafik%22">Guefaifia, Rafik</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> r.guefaifia@qu.edu.sa</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Fixed+Point+Theory+%26+Algorithms+for+Sciences+%26+Engineering%22">Fixed Point Theory & Algorithms for Sciences & Engineering</searchLink>. 4/14/2026, Vol. 2026 Issue 1, p1-12. 12p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Vector+valued+functions%22">Vector valued functions</searchLink><br /><searchLink fieldCode="DE" term="%22Fractal+analysis%22">Fractal analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+error%22">Approximation error</searchLink><br /><searchLink fieldCode="DE" term="%22Weierstrass-Stone+theorem%22">Weierstrass-Stone theorem</searchLink><br /><searchLink fieldCode="DE" term="%22Continuous+functions%22">Continuous functions</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this article, we first prove the existence of a class of vector-valued and multivariate α-fractal functions on a hype-rectangle of R q . After that, we show that the set of functions with any possible fixed dimension in the continuous function space is dense with respect to uniform norm. Building on this, we also study dimension preserving approximation in this general setting. We then introduce and study some constrained approximation aspects based on dimension-preserving notion. Further, we prove some approximation theoretic results (such as Weierstrass approximation theorem) of the constructed vector-valued and multivariate α-fractal functions on a hype-rectangle of R q . In particular, we show the existence of a dense subset of α-fractal functions in the continuous functions space. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Fixed Point Theory & Algorithms for Sciences & Engineering is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1186/s13663-026-00837-5 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 12 StartPage: 1 Subjects: – SubjectFull: Vector valued functions Type: general – SubjectFull: Fractal analysis Type: general – SubjectFull: Approximation error Type: general – SubjectFull: Weierstrass-Stone theorem Type: general – SubjectFull: Continuous functions Type: general Titles: – TitleFull: Existence of a class of vector-valued and multivariate α-fractal functions on a hype-rectangle of Rq. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Verma, Shubham Kumar – PersonEntity: Name: NameFull: Boulaaras, Salah – PersonEntity: Name: NameFull: Guefaifia, Rafik IsPartOfRelationships: – BibEntity: Dates: – D: 14 M: 04 Text: 4/14/2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 27305422 Numbering: – Type: volume Value: 2026 – Type: issue Value: 1 Titles: – TitleFull: Fixed Point Theory & Algorithms for Sciences & Engineering Type: main |
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