Israel Journal of Mathematics

, Volume 26, Issue 2, pp 197–204

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


  • A. Pazy
    • Institute of MathematicsThe Hebrew University of Jerusalem

DOI: 10.1007/BF03007669

Cite this article as:
Pazy, A. Israel J. Math. (1977) 26: 197. doi:10.1007/BF03007669


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 sequenceTnx and the sequenceSnx of the arithmetical means of the sequenceTnx, asn → ∞. We also give some results concerning the strong convergence ofSnx.

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© Hebrew University 1977