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On the convex approximation property and the asymptotic behavior of nonlinear contractions in Banach spaces. (English) Zbl 0475.47037

MSC:
47H09Mappings defined by “shrinking” properties
46B99Normed linear spaces and Banach spaces
References:
[1]J. B. Baillon,Un théorème de type ergodique pour les contractions nonlinéaires dans un espace de Hilbert, C. R. Acad. Sci. Paris280 (1975), 1511–1514.
[2]J. B. Baillon, Thèse, Université de Paris VI, 1978.
[3]B. Beauzamy et P. Enflo,Théorèmes de point fixe et d’approximation, preprint.
[4]F. Browder,Nonlinear Operators and Nonlinear Equations of Evolution in Banach Spaces, Proc. Symposia Pure Math. XVIII, pt. 2, Amer. Math. Soc., Providence, R.I., 1976.
[5]R. E. Bruck,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 (1978), 1–16. · Zbl 0367.47037 · doi:10.1007/BF02760397
[6]R. E. Bruck,A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces, Israel J. Math.32 (1979), 279–282. · Zbl 0423.47024 · doi:10.1007/BF02764907
[7]R. E. Bruck and G. B. Passty,Almost convergence of the infinite product of resolvents in Banach spaces, Nonlinear Analysis3 (1979), 279–282. · Zbl 0407.47035 · doi:10.1016/0362-546X(79)90083-X
[8]D. P. Giesy,On a convexity condition in normed linear spaces, Trans. Amer. Math. Soc.125, (1966), 114–146. · doi:10.1090/S0002-9947-1966-0205031-7
[9]G. Pisier,Sur les espaces de Banch qui ne contiennent pas uniformement de l l m . C.R. Acad. Sci. Paris277 (1973), A991-A994.
[10]S. Reich,Nonlinear evolution equations and nonlinear ergodic theorems, Nonlinear Analysis1 (1977), 319–330. · Zbl 0359.34059 · doi:10.1016/S0362-546X(97)90001-8
[11]S. Reich,Almost convergence and nonlinear ergodic theorems, J. Approximation Theory24 (1978), 269–272. · Zbl 0404.47032 · doi:10.1016/0021-9045(78)90012-6
[12]E. H. Zarantonello,Protections on convex sets in Hilbert space and spectral theory, inContributions to Nonlinear Functional Analysis, Academic Press, New York, 1971, pp. 237–244.