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Approximation of fixed points of nonexpansive mappings. (English) Zbl 0797.47036
The author considers an iteration procedure due to {\it B. Halpern} [Bull. Am. Math. Soc. 73, 957-961 (1967; Zbl 0177.191)] for nonlinear maps in a Hilbert space.

47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47H09Mappings defined by “shrinking” properties
Full Text: DOI
[1] F. E. Browder, Convergence of approximants to fixed points of nonlinear maps in Banach spaces. Arch. Rational Mech. Anal.24, 82-90 (1967). · Zbl 0148.13601 · doi:10.1007/BF00251595
[2] B. Halpern, Fixed points of nonexpanding maps. Bull. Amer. Math. Soc.73, 957-961 (1967). · Zbl 0177.19101 · doi:10.1090/S0002-9904-1967-11864-0
[3] U.Krengel, Ergodic Theorems. Berlin-New York 1985.
[4] M.Lin and R.Wittmann, Pointwise ergodic theorems for certain order preserving mappings inL 1. In: A. Bellow and R. L. Jones, Almost every where convergence. 191-207, London-New York-San Francisco 1991. · Zbl 0759.47006
[5] S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces. J. Math. Anal. Appl.75, 287-292 (1980). · Zbl 0437.47047 · doi:10.1016/0022-247X(80)90323-6
[6] R. Wittmann, Hopf’s ergodic theorem for nonlinear operators. Math. Ann.289, 239-253 (1991). · Zbl 0716.47028 · doi:10.1007/BF01446570