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/
| Summary: | 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. |
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