Asymptotic Behavior of Relatively Nonexpansive Operators in Banach Spaces 论文

摘要

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 ƒ on X . We prove (under certain assumptions on ƒ) that the iterates of a generic mapping in these spaces converge strongly to a retraction onto F .