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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.