Abstract
LetT be a nonexpansive self-mapping of a closed convex subsetC of a real Hilbert space. In this paper we deal with the structure of the weak ω-limit set of iterates {T nx}, establish conditions under which it is invariant underT, and show that {T nx} converges weakly iffT has a fixed-point andT nx-Tn+1x→0 weakly.
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Dedicated to the memory of my father
Supported by NSF Grant MCS 76-08217.
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Bruck, R.E. On the almost-convergence of iterates of a nonexpansive mapping in Hilbert space and the structure of the weak ω-limit set. Israel J. Math. 29, 1–16 (1978). https://doi.org/10.1007/BF02760397
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DOI: https://doi.org/10.1007/BF02760397