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...
- Autores:
-
Uyi 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
- http://creativecommons.org/licenses/by-nc-nd/2.5/co/
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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 |
Uyi Afuwape, Anthony Balla, M. Y. Udo-utun, Xavier |
| dc.contributor.author.none.fl_str_mv |
Uyi Afuwape, Anthony Balla, M. Y. Udo-utun, Xavier |
| 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 |
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info:eu-repo/semantics/article |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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Artículo de investigación |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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publishedVersion |
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1224-1784 |
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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 |
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http://hdl.handle.net/10495/25444 |
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eng |
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eng |
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openAccess |
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http://creativecommons.org/licenses/by-nc-nd/2.5/co/ http://purl.org/coar/access_right/c_abf2 https://creativecommons.org/licenses/by-nc-nd/4.0/ |
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Universitatea „Ovidius” din Constanța |
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Modelación con Ecuaciones Diferenciales |
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Constanza, Rumanía |
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Universidad de Antioquia |
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Uyi Afuwape, AnthonyBalla, M. Y.Udo-utun, Xavier2022-01-21T14:38:47Z2022-01-21T14:38:47Z20121224-1784http://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 ConstanțaModelación con Ecuaciones DiferencialesConstanza, Rumaníainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_2df8fbb1https://purl.org/redcol/resource_type/ARTArtículo de investigaciónhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/2.5/co/http://purl.org/coar/access_right/c_abf2https://creativecommons.org/licenses/by-nc-nd/4.0/Approximate Cycles of the Second Kind in Hilbert space for a Generalized Barbashin-Ezeilo ProblemEcuaciones de VolterraVolterra equationsEspacio de HilbertHilbert spaceEspacio de BanachBanach spacesAnalele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica514201ORIGINALUdoutunXavier_2012_ApproximateCyclesSecond.pdfUdoutunXavier_2012_ApproximateCyclesSecond.pdfArtículo de investigaciónapplication/pdf120301https://bibliotecadigital.udea.edu.co/bitstream/10495/25444/1/UdoutunXavier_2012_ApproximateCyclesSecond.pdfdd7cc11087a2e5c8c7012e0a00ff21c4MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8823https://bibliotecadigital.udea.edu.co/bitstream/10495/25444/2/license_rdfb88b088d9957e670ce3b3fbe2eedbc13MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://bibliotecadigital.udea.edu.co/bitstream/10495/25444/3/license.txt8a4605be74aa9ea9d79846c1fba20a33MD5310495/25444oai:bibliotecadigital.udea.edu.co:10495/254442022-09-02 13:09:39.679Repositorio Institucional Universidad de Antioquiaandres.perez@udea.edu.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 |