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A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces. (English) Zbl 0423.47024


MSC:

47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
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References:

[1] J. B. Baillon, untitled preprint.
[2] J. B. Baillon, R. E. Bruck and S. Reich,On the asymptotic behavior of nonexpansive mappings and semigroups in Banach spaces, to appear in Houston J. Math. · Zbl 0396.47033
[3] F. E. Browder,Nonlinear operators and nonlinear equationas of evolution in Banach spaces, Proc. Symposia Pure Math. XVIII, pt. 2, Amer. Math. Soc., Providence, R. I., 1976.
[4] Bruck, R. E., Construction of periodic solution of periodic contractive evolution systems, Notices Amer. Math. Soc., 24, A-474 (1977)
[5] 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) · Zbl 0367.47037 · doi:10.1007/BF02760397
[6] DeMarr, R., Common fixed points for commuting contraction mappings, Pacific J. Math., 13, 1139-1141 (1963) · Zbl 0191.14901
[7] Lorentz, G. G., A contribution to the theory of divergent series, Acta Math., 80, 167-190 (1948) · Zbl 0031.29501 · doi:10.1007/BF02393648
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