Iterative approximation of fixed points and applications to two-point second-order boundary value problems and to machine learning

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dc.authoridMilovanovic, Gradimir/0000-0002-3255-8127
dc.authoridHacioglu, Emirhan/0000-0003-0195-1935
dc.authoridMaldar, Samet/0000-0002-2083-899X
dc.authoridGURSOY, Faik/0000-0002-7118-9088
dc.authorwosidMilovanovic, Gradimir/C-2444-2015
dc.authorwosidGürsoy, Faik/AAW-6186-2021
dc.authorwosidHACIOĞLU, Emirhan/KGM-0096-2024
dc.contributor.authorHacioglu, Emirhan
dc.contributor.authorGursoy, Faik
dc.contributor.authorMaldar, Samet
dc.contributor.authorAtalan, Yunus
dc.contributor.authorMilovanovic, Gradimir V.
dc.date.accessioned2024-06-12T10:58:27Z
dc.date.available2024-06-12T10:58:27Z
dc.date.issued2021
dc.departmentTrakya Üniversitesien_US
dc.description.abstractIn this paper, we revisit two recently published papers on the iterative approximation of fixed points by Kumam et al. (2019) [17] and Maniu (2020) [19] and reproduce convergence, stability, and data dependency results presented in these papers by removing some strong restrictions imposed on parametric control sequences. We confirm the validity and applicability of our results through various non-trivial numerical examples. We suggest a new method based on the iteration algorithm given by Thakur et al. (2014) [28] to solve the two-point second-order boundary value problems. Furthermore, based on the above mentioned iteration algorithm and S-iteration algorithm, we propose two new gradient type projection algorithms and applied them to supervised learning. In both applications, we present some numerical examples to demonstrate the superiority of the newly introduced methods in terms of convergence, accuracy, and computational time against some earlier methods. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.en_US
dc.description.sponsorshipSerbian Academy of Sciences and Arts [Phi-96]en_US
dc.description.sponsorshipThe work of G.V. Milovanovi ' c was supported in part by the Serbian Academy of Sciences and Arts (Project Phi-96).en_US
dc.identifier.doi10.1016/j.apnum.2021.04.020
dc.identifier.endpage172en_US
dc.identifier.issn0168-9274
dc.identifier.issn1873-5460
dc.identifier.scopus2-s2.0-85105582260en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage143en_US
dc.identifier.urihttps://doi.org/10.1016/j.apnum.2021.04.020
dc.identifier.urihttps://hdl.handle.net/20.500.14551/20074
dc.identifier.volume167en_US
dc.identifier.wosWOS:000657863200008en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherElsevieren_US
dc.relation.ispartofApplied Numerical Mathematicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectConvergenceen_US
dc.subjectStabilityen_US
dc.subjectData Dependenceen_US
dc.subjectBoundary Value Problemen_US
dc.subjectSupervised Learningen_US
dc.subjectMachine Learningen_US
dc.subjectConvergenceen_US
dc.titleIterative approximation of fixed points and applications to two-point second-order boundary value problems and to machine learningen_US
dc.typeArticleen_US

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