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Some remarks on the fixed point stability for nonexpansive mappings. (English) Zbl 0764.47035

The article presents some conditions under which the weak limit \(x\) of the sequence of fixed points \(x_ n\) for nonexpansive mappings \(T_ n\) of a nonempty weakly closed subsets of some Banach space \(X\) into a family of nonempty closed subsets of \(X\) is a fixed point for another nonexpansive mapping \(T\).
Reviewer: P.Zabreiko (Minsk)

MSC:

47J25 Iterative procedures involving nonlinear operators
46B20 Geometry and structure of normed linear spaces
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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