Abstract
LetT be a nonexpansive mapping on a closed convex subsetC of a real Hilbert spaceH. In the present note we deal with the weak convergence of the sequenceT n x and the sequenceS n x of the arithmetical means of the sequenceT n x, asn → ∞. We also give some results concerning the strong convergence ofS n x.
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Pazy, A. On the asymptotic behavior of iterates of nonexpansive mappings in Hilbert space. Israel J. Math. 26, 197–204 (1977). https://doi.org/10.1007/BF03007669
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DOI: https://doi.org/10.1007/BF03007669