Aproximate 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 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

Keywords

• approximate cycles of the second kind
• generalized barbashin-ezeilo problem
• volterra integral operator
• pseudocontractive maps in hilbert spaces