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dc.contributor.author
Sofonea, Mircea  
dc.contributor.author
Tarzia, Domingo Alberto  
dc.date.available
2024-03-19T13:23:36Z  
dc.date.issued
2024-02  
dc.identifier.citation
Sofonea, Mircea; Tarzia, Domingo Alberto; Convergence Criteria for Fixed Point Problems and Differential Equations; MDPI; Mathematics; 12; 3; 2-2024; 1-19  
dc.identifier.issn
2227-7390  
dc.identifier.uri
http://hdl.handle.net/11336/230908  
dc.description.abstract
We consider a Cauchy problem for differential equations in a Hilbert space X. The problem is stated in a time interval I, which can be finite or infinite. We use a fixed point argument for history-dependent operators to prove the unique solvability of the problem. Then, we establish convergence criteria for both a general fixed point problem and the corresponding Cauchy problem. These criteria provide the necessary and sufficient conditions on a sequence (Formula presented.), which guarantee its convergence to the solution of the corresponding problem, in the space of both continuous and continuously differentiable functions. We then specify our results in the study of a particular differential equation governed by two nonlinear operators. Finally, we provide an application in viscoelasticity and give a mechanical interpretation of the corresponding convergence result.  
dc.format
application/pdf  
dc.language.iso
eng  
dc.publisher
MDPI  
dc.rights
info:eu-repo/semantics/openAccess  
dc.rights.uri
https://creativecommons.org/licenses/by/2.5/ar/  
dc.subject
CAUCHY PROBLEM  
dc.subject
CONVERGENCE CRITERION  
dc.subject
DIFFERENTIAL EQUATION  
dc.subject
FIXED POINT  
dc.subject
HISTORY-DEPENDENT OPERATOR  
dc.subject
VISCOELASTIC CONSTITUTIVE LAW  
dc.subject.classification
Matemática Aplicada  
dc.subject.classification
Matemáticas  
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS  
dc.title
Convergence Criteria for Fixed Point Problems and Differential Equations  
dc.type
info:eu-repo/semantics/article  
dc.type
info:ar-repo/semantics/artículo  
dc.type
info:eu-repo/semantics/publishedVersion  
dc.date.updated
2024-03-19T10:24:56Z  
dc.journal.volume
12  
dc.journal.number
3  
dc.journal.pagination
1-19  
dc.journal.pais
Estados Unidos  
dc.description.fil
Fil: Sofonea, Mircea. Université de Perpignan Via Domitia; Francia  
dc.description.fil
Fil: Tarzia, Domingo Alberto. Universidad Austral; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina  
dc.journal.title
Mathematics  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.3390/math12030395