Approximate Cycles of the Second Kind in Hilbert space for a Generalized Barbashin-Ezeilo Problem

ABSTRACT: In this work we show that the Volterra integral operator defined on the space of absolutely stable functions induces an asymptotically pseudocontractive operator. We, then, show that Afuwape’s [1] generalization of the Barbashin-Ezeilo problem is solvable in a Banach space (but not in Hilb...

Full description

Autores:
Afuwape Afuwape, Anthony
Balla, M. Y.
Udo-utun, Xavier
Tipo de recurso:
Article of investigation
Fecha de publicación:
2012
Institución:
Universidad de Antioquia
Repositorio:
Repositorio UdeA
Idioma:
eng
OAI Identifier:
oai:bibliotecadigital.udea.edu.co:10495/25444
Acceso en línea:
http://hdl.handle.net/10495/25444
Palabra clave:
Ecuaciones de Volterra
Volterra equations
Espacio de Hilbert
Hilbert space
Espacio de Banach
Banach spaces
Rights
openAccess
License
https://creativecommons.org/licenses/by-nc-nd/4.0/
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network_acronym_str UDEA2
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dc.title.spa.fl_str_mv Approximate Cycles of the Second Kind in Hilbert space for a Generalized Barbashin-Ezeilo Problem
title Approximate Cycles of the Second Kind in Hilbert space for a Generalized Barbashin-Ezeilo Problem
spellingShingle Approximate Cycles of the Second Kind in Hilbert space for a Generalized Barbashin-Ezeilo Problem
Ecuaciones de Volterra
Volterra equations
Espacio de Hilbert
Hilbert space
Espacio de Banach
Banach spaces
title_short Approximate Cycles of the Second Kind in Hilbert space for a Generalized Barbashin-Ezeilo Problem
title_full Approximate Cycles of the Second Kind in Hilbert space for a Generalized Barbashin-Ezeilo Problem
title_fullStr Approximate Cycles of the Second Kind in Hilbert space for a Generalized Barbashin-Ezeilo Problem
title_full_unstemmed Approximate Cycles of the Second Kind in Hilbert space for a Generalized Barbashin-Ezeilo Problem
title_sort Approximate Cycles of the Second Kind in Hilbert space for a Generalized Barbashin-Ezeilo Problem
dc.creator.fl_str_mv Afuwape Afuwape, Anthony
Balla, M. Y.
Udo-utun, Xavier
dc.contributor.author.none.fl_str_mv Afuwape Afuwape, Anthony
Balla, M. Y.
Udo-utun, Xavier
dc.contributor.researchgroup.spa.fl_str_mv Modelación con Ecuaciones Diferenciales
dc.subject.lemb.none.fl_str_mv Ecuaciones de Volterra
Volterra equations
Espacio de Hilbert
Hilbert space
Espacio de Banach
Banach spaces
topic Ecuaciones de Volterra
Volterra equations
Espacio de Hilbert
Hilbert space
Espacio de Banach
Banach spaces
description ABSTRACT: In this work we show that the Volterra integral operator defined on the space of absolutely stable functions induces an asymptotically pseudocontractive operator. We, then, show that Afuwape’s [1] generalization of the Barbashin-Ezeilo problem is solvable in a Banach space (but not in Hilbert space L2[0, ∞)). However applying Osilike-Akuchu[10] theorem and recent results (in Hilbert space) of Igbokwe and Udoutun[8] we formulate conditions for finding approximate cycles of the second kind (in the Hilbert space W2,20 [0, ∞)) to this problem given in the form x′′′ + ax′′ + g(x′) + φ(x) = 0.
publishDate 2012
dc.date.issued.none.fl_str_mv 2012
dc.date.accessioned.none.fl_str_mv 2022-01-21T14:38:47Z
dc.date.available.none.fl_str_mv 2022-01-21T14:38:47Z
dc.type.spa.fl_str_mv Artículo de investigación
dc.type.coar.spa.fl_str_mv http://purl.org/coar/resource_type/c_2df8fbb1
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dc.identifier.issn.none.fl_str_mv 1224-1784
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/10495/25444
dc.identifier.doi.none.fl_str_mv 10.2478/v10309-012-0001-z
dc.identifier.eissn.none.fl_str_mv 1844-0835
identifier_str_mv 1224-1784
10.2478/v10309-012-0001-z
1844-0835
url http://hdl.handle.net/10495/25444
dc.language.iso.spa.fl_str_mv eng
language eng
dc.relation.citationendpage.spa.fl_str_mv 14
dc.relation.citationissue.spa.fl_str_mv 1
dc.relation.citationstartpage.spa.fl_str_mv 5
dc.relation.citationvolume.spa.fl_str_mv 20
dc.relation.ispartofjournal.spa.fl_str_mv Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica
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dc.publisher.spa.fl_str_mv Universitatea „Ovidius” din Constanța
dc.publisher.place.spa.fl_str_mv Constanza, Rumanía
institution Universidad de Antioquia
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spelling Afuwape Afuwape, AnthonyBalla, M. Y.Udo-utun, XavierModelación con Ecuaciones Diferenciales2022-01-21T14:38:47Z2022-01-21T14:38:47Z20121224-1784http://hdl.handle.net/10495/2544410.2478/v10309-012-0001-z1844-0835ABSTRACT: In this work we show that the Volterra integral operator defined on the space of absolutely stable functions induces an asymptotically pseudocontractive operator. We, then, show that Afuwape’s [1] generalization of the Barbashin-Ezeilo problem is solvable in a Banach space (but not in Hilbert space L2[0, ∞)). However applying Osilike-Akuchu[10] theorem and recent results (in Hilbert space) of Igbokwe and Udoutun[8] we formulate conditions for finding approximate cycles of the second kind (in the Hilbert space W2,20 [0, ∞)) to this problem given in the form x′′′ + ax′′ + g(x′) + φ(x) = 0.COL002436510application/pdfengUniversitatea „Ovidius” din ConstanțaConstanza, Rumaníahttps://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/2.5/co/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Approximate Cycles of the Second Kind in Hilbert space for a Generalized Barbashin-Ezeilo ProblemArtículo de investigaciónhttp://purl.org/coar/resource_type/c_2df8fbb1https://purl.org/redcol/resource_type/ARThttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionEcuaciones de VolterraVolterra equationsEspacio de HilbertHilbert spaceEspacio de BanachBanach spaces141520Analele Stiintifice ale Universitatii Ovidius Constanta, Seria MatematicaPublicationORIGINALUdoutunXavier_2012_ApproximateCyclesSecond.pdfUdoutunXavier_2012_ApproximateCyclesSecond.pdfArtículo de investigaciónapplication/pdf120301https://bibliotecadigital.udea.edu.co/bitstreams/76cdbddc-89a3-4345-b4ee-f0fbf024f3b5/downloaddd7cc11087a2e5c8c7012e0a00ff21c4MD51trueAnonymousREADCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8823https://bibliotecadigital.udea.edu.co/bitstreams/c062b97a-f4ad-4a73-aabc-76a514e37d55/downloadb88b088d9957e670ce3b3fbe2eedbc13MD52falseAnonymousREADLICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://bibliotecadigital.udea.edu.co/bitstreams/e9b5621a-3d3b-47d0-a1bf-2957b4cdc9ca/download8a4605be74aa9ea9d79846c1fba20a33MD53falseAnonymousREADTEXTUdoutunXavier_2012_ApproximateCyclesSecond.pdf.txtUdoutunXavier_2012_ApproximateCyclesSecond.pdf.txtExtracted texttext/plain16134https://bibliotecadigital.udea.edu.co/bitstreams/502e5af6-0f78-4a9b-8bb8-d034a6a62b6d/downloadd58e39fdaa65dcb7cfd4a49ea201009cMD54falseAnonymousREADTHUMBNAILUdoutunXavier_2012_ApproximateCyclesSecond.pdf.jpgUdoutunXavier_2012_ApproximateCyclesSecond.pdf.jpgGenerated Thumbnailimage/jpeg8119https://bibliotecadigital.udea.edu.co/bitstreams/2d07a42f-7a62-4d0e-8208-b99fe332d93f/downloadc1cd02ef6af95d3df855446cfe2c2c18MD55falseAnonymousREAD10495/25444oai:bibliotecadigital.udea.edu.co:10495/254442025-03-26 19:47:48.758https://creativecommons.org/licenses/by-nc-nd/4.0/open.accesshttps://bibliotecadigital.udea.edu.coRepositorio Institucional de la Universidad de Antioquiaaplicacionbibliotecadigitalbiblioteca@udea.edu.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