, Volume 26, Issue 2, pp 197-204

On the asymptotic behavior of iterates of nonexpansive mappings in Hilbert space

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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.