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Asymptotic behavior of relatively nonexpansive operators in Banach spaces. (English) Zbl 1010.47032
Let K be a closed convexed subset of a Banach space X, and let F be a nonempty closed subset of K. The authors 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. The aim of this paper is to prove that under quite mild conditions on F strong convergence of the sequences {T k x} k=1 generated by relatively nonexpansive mappings is the rule and that weak, but not strong convergence is the exception.

47H09Mappings defined by “shrinking” properties
49M30Other numerical methods in calculus of variations
52A41Convex functions and convex programs (convex geometry)