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Asymptotic behavior of quasi-nonexpansive mappings

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DOI: 10.1016/s1570-579x(01)80006-9

Abstract

Let K be a closed convex subset of a Banach space X and let F be a nonempty closedconvex subset of K. We consider complete metric spaces of self-mappings of K which fix all the points of F and are quasi-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 on F.

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