Fixed point iteration for local strictly pseudo-contractive mapping. (English) Zbl 0734.47042

The author studies iterates of locally strictly pseudo-contractive mappings in uniformly smooth Banach spaces and their convergence to fixed points.


47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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[1] Ya. I. Al’ber and A. I. Notik, Geometric properties of Banach spaces and approximate methods for solving nonlinear operator equations, Soviet Math. Dokl. 29 (1984), 611-615. · Zbl 0591.47051
[2] C. E. Chidume, Iterative approximation of fixed points of Lipschitzian strictly pseudocontractive mappings, Proc. Amer. Math. Soc. 99 (1987), no. 2, 283 – 288. · Zbl 0646.47037
[3] Tosio Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan 19 (1967), 508 – 520. · Zbl 0163.38303
[4] Simeon Reich, An iterative procedure for constructing zeros of accretive sets in Banach spaces, Nonlinear Anal. 2 (1978), no. 1, 85 – 92. · Zbl 0375.47032
[5] -, Constructive techniques for accretive and monotone operators, Appl. Nonlinear Anal. Arlington, TX, 1979. · Zbl 0444.47042
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