<abstract xmlns="http://www.w3.org/1999/xhtml"> 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-Akuchuf[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 W02,2[0,∞)) to this problem given in the form x'" + ax" + g(x') + φ(x)= 0</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-Akuchuf[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 W02,2[0,∞)) to this problem given in the form x'" + ax" + g(x') + φ(x)= 0

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

Instituto de Matemáticas, Universidad de Antioquia, Calle 67, No. 53-108, Medellín AA 1226,Colombia

Department of Mathematics and Statistics, University of Maiduguri, Nigeria

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

In this work we show that the Volterra integral operator defined on the space of absolutely stable functions induces an asymptotically pseudocontractive...

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

Published Online: May 17, 2013

Page range: 5 - 14

DOI: https://doi.org/10.2478/v10309-012-0001-z

Keywords
approximate cycles of the second kind, generalized Barbashin-Ezeilo problem, Volterra Integral operator, pseudocontractive maps in Hilbert spaces

This content is open access.

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

Published Online: May 17, 2013

Page range: 5 - 14

DOI: https://doi.org/10.2478/v10309-012-0001-z

Keywordsapproximate cycles of the second kind, generalized Barbashin-Ezeilo problem, Volterra Integral operator, pseudocontractive maps in Hilbert spaces

This content is open access.

Keywords
approximate cycles of the second kind, generalized Barbashin-Ezeilo problem, Volterra Integral operator, pseudocontractive maps in Hilbert spaces