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2 Journal of Applied Analysis

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Asymptotic behavior of inexact orbits for a class of operators in complete metric spaces

Butnariu D., Reich S., Zaslavski A. J.

Journal of Applied Analysis

2007

Vol. 13, nr 1

1-11

We exhibit a class of nonlinear operators with the property that their iterates converge to their unique fixed points even when com- putational errors are present. We also showthat most (in the sense of the Baire category) elements in an appropriate complete metric space of operators do, in fact, possess this property.

Asymptotic behavior of relatively nonexpansive operators in Banach spaces

Butnariu D., Reich S., Zaslavski A. J.

Journal of Applied Analysis

2001

Vol. 7, nr 2

151-174

Let K be a closed convex subset of a Banach space X and let F be a nonempty closed convex subset of K. We consider complete metric spaces of self-mappings of K which fix all the points of F and are relatively nonexpansive with respect to a given convex function f on X. We prove (under certain assumptions on f) that the iterates of a generic mapping in these spaces converge strongly to a retraction onto F.