A Generalized Topology Approach to Trajectory Convergence in Nonautonomous Evolution Equations With Monotone Operators.
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| Title: | A Generalized Topology Approach to Trajectory Convergence in Nonautonomous Evolution Equations With Monotone Operators. |
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| Authors: | Abbas, Boushra1 (AUTHOR) boushraabbas@latakia-univ.edu.sy, Reich, Simeon1 (AUTHOR) sreich@techunix.technion.ac.il |
| Source: | Abstract & Applied Analysis. 3/3/2026, Vol. 2026, p1-7. 7p. |
| Subjects: | Topology, Evolution equations, Hilbert space, Monotone operators, Mathematical optimization, Image denoising |
| Abstract: | This paper investigates the application of β‐open sets to the convergence analysis of nonautonomous evolution equations governed by maximal monotone operators in Hilbert spaces. β‐open sets are a class of generalized open sets introduced by Njåstad (1965), which coincides with the class of semiopen sets by Levine (1963). We first examine whether the properties of β‐open sets, which form a generalized topology (not a classical topology), can offer a more flexible framework for studying trajectory convergence. And then we discuss potential advantages in relaxing certain coercivity conditions in contrast with analyses in standard metric or weak topologies, while addressing the non‐Hausdorff nature and limited intersection closure of β‐open sets. Examples from optimization problems (variational inequalities and sparse regression) and numerical insights from image denoising applications are utilized to illustrate the benefits of the approach. The paper highlights key challenges and outlines directions for further theoretical and computational development. [ABSTRACT FROM AUTHOR] |
| Copyright of Abstract & Applied Analysis is the property of Wiley-Blackwell 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: 192000670 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A Generalized Topology Approach to Trajectory Convergence in Nonautonomous Evolution Equations With Monotone Operators. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Abbas%2C+Boushra%22">Abbas, Boushra</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> boushraabbas@latakia-univ.edu.sy</i><br /><searchLink fieldCode="AR" term="%22Reich%2C+Simeon%22">Reich, Simeon</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> sreich@techunix.technion.ac.il</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Abstract+%26+Applied+Analysis%22">Abstract & Applied Analysis</searchLink>. 3/3/2026, Vol. 2026, p1-7. 7p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Topology%22">Topology</searchLink><br /><searchLink fieldCode="DE" term="%22Evolution+equations%22">Evolution equations</searchLink><br /><searchLink fieldCode="DE" term="%22Hilbert+space%22">Hilbert space</searchLink><br /><searchLink fieldCode="DE" term="%22Monotone+operators%22">Monotone operators</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Image+denoising%22">Image denoising</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper investigates the application of β‐open sets to the convergence analysis of nonautonomous evolution equations governed by maximal monotone operators in Hilbert spaces. β‐open sets are a class of generalized open sets introduced by Njåstad (1965), which coincides with the class of semiopen sets by Levine (1963). We first examine whether the properties of β‐open sets, which form a generalized topology (not a classical topology), can offer a more flexible framework for studying trajectory convergence. And then we discuss potential advantages in relaxing certain coercivity conditions in contrast with analyses in standard metric or weak topologies, while addressing the non‐Hausdorff nature and limited intersection closure of β‐open sets. Examples from optimization problems (variational inequalities and sparse regression) and numerical insights from image denoising applications are utilized to illustrate the benefits of the approach. The paper highlights key challenges and outlines directions for further theoretical and computational development. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Abstract & Applied Analysis is the property of Wiley-Blackwell 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: 10.1155/aaa/8495254 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 7 StartPage: 1 Subjects: – SubjectFull: Topology Type: general – SubjectFull: Evolution equations Type: general – SubjectFull: Hilbert space Type: general – SubjectFull: Monotone operators Type: general – SubjectFull: Mathematical optimization Type: general – SubjectFull: Image denoising Type: general Titles: – TitleFull: A Generalized Topology Approach to Trajectory Convergence in Nonautonomous Evolution Equations With Monotone Operators. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Abbas, Boushra – PersonEntity: Name: NameFull: Reich, Simeon IsPartOfRelationships: – BibEntity: Dates: – D: 03 M: 03 Text: 3/3/2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 10853375 Numbering: – Type: volume Value: 2026 Titles: – TitleFull: Abstract & Applied Analysis Type: main |
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