Time Scale Henstock-Kurzweil Integration for Set-Valued Functions.
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| Title: | Time Scale Henstock-Kurzweil Integration for Set-Valued Functions. |
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| Authors: | Sekhose, Vikuozonuo1 vikuosekhose4@gmail.com, Bharali, Hemen2 hemen.bharali@gmail.com |
| Source: | IAENG International Journal of Applied Mathematics. Apr2026, Vol. 56 Issue 4, p1332-1343. 12p. |
| Subjects: | Integrals, Set functions, Mathematical functions, Convex domains, Hausdorff measures |
| Abstract: | This paper introduces the Henstock-Kurzweil integration for functions whose values are sets on time scales- the set-valued Henstock-Kurzweil Δ-integral and set-valued Henstock-Kurzweil ∇-integral. Properties of the integral are established. Some key theorems in the paper discusses convexity, relation between set-valued Henstock-Kurzweil integral and ordinary Henstock-Kurzweil integral via support function, singleton set function and Hausdorff metric respectively. The convergence of sequences and series of set-valued Henstock-Kurzweil integrable functions are also formulated. In addition, as a linear combination of the Δ- and ∇-integrals we introduce the set-valued Henstock-Kurzweil ♢α-integral and conclude with a theorem depicting the relation between the three integrals. [ABSTRACT FROM AUTHOR] |
| Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) 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: 192720721 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Time Scale Henstock-Kurzweil Integration for Set-Valued Functions. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Sekhose%2C+Vikuozonuo%22">Sekhose, Vikuozonuo</searchLink><relatesTo>1</relatesTo><i> vikuosekhose4@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Bharali%2C+Hemen%22">Bharali, Hemen</searchLink><relatesTo>2</relatesTo><i> hemen.bharali@gmail.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. Apr2026, Vol. 56 Issue 4, p1332-1343. 12p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Integrals%22">Integrals</searchLink><br /><searchLink fieldCode="DE" term="%22Set+functions%22">Set functions</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+functions%22">Mathematical functions</searchLink><br /><searchLink fieldCode="DE" term="%22Convex+domains%22">Convex domains</searchLink><br /><searchLink fieldCode="DE" term="%22Hausdorff+measures%22">Hausdorff measures</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper introduces the Henstock-Kurzweil integration for functions whose values are sets on time scales- the set-valued Henstock-Kurzweil Δ-integral and set-valued Henstock-Kurzweil ∇-integral. Properties of the integral are established. Some key theorems in the paper discusses convexity, relation between set-valued Henstock-Kurzweil integral and ordinary Henstock-Kurzweil integral via support function, singleton set function and Hausdorff metric respectively. The convergence of sequences and series of set-valued Henstock-Kurzweil integrable functions are also formulated. In addition, as a linear combination of the Δ- and ∇-integrals we introduce the set-valued Henstock-Kurzweil ♢α-integral and conclude with a theorem depicting the relation between the three integrals. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) 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: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 12 StartPage: 1332 Subjects: – SubjectFull: Integrals Type: general – SubjectFull: Set functions Type: general – SubjectFull: Mathematical functions Type: general – SubjectFull: Convex domains Type: general – SubjectFull: Hausdorff measures Type: general Titles: – TitleFull: Time Scale Henstock-Kurzweil Integration for Set-Valued Functions. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Sekhose, Vikuozonuo – PersonEntity: Name: NameFull: Bharali, Hemen IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: Apr2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 19929978 Numbering: – Type: volume Value: 56 – Type: issue Value: 4 Titles: – TitleFull: IAENG International Journal of Applied Mathematics Type: main |
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