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

Abstract

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.