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Weak convergence to the fixed point of an asymptotically nonexpansive map. (English) Zbl 0377.47037


MSC:

47H10 Fixed-point theorems
46B99 Normed linear spaces and Banach spaces; Banach lattices
54C05 Continuous maps
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References:

[1] S. C. Bose, On nonexpansive and asymptotically nonexpansive mappings (unpublished work).
[2] E. Lami Dozo, Multivalued nonexpansive mappings and Opial’s condition, Proc. Amer. Math. Soc. 38 (1973), 286 – 292. · Zbl 0268.47060
[3] Michael Edelstein, Fixed point theorems in uniformly convex Banach spaces, Proc. Amer. Math. Soc. 44 (1974), 369 – 374. · Zbl 0286.47035
[4] Michael Edelstein, The construction of an asymptotic center with a fixed-point property, Bull. Amer. Math. Soc. 78 (1972), 206 – 208. · Zbl 0231.47029
[5] K. Goebel and W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), 171 – 174. · Zbl 0256.47045
[6] W. A. Kirk, On nonlinear mappings of strongly semicontractive type, J. Math. Anal. Appl. 27 (1969), 409 – 412. · Zbl 0183.15103
[7] Zdzisław Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591 – 597. · Zbl 0179.19902
[8] -, Lecture notes on nonexpansive and monotone mappings in Banach spaces, Center for Dynamical Systems, Brown University, Providence, R. I., 1967.
[9] Helmut Schaefer, Über die Methode sukzessiver Approximationen, Jber. Deutsch. Math. Verein. 59 (1957), no. Abt. 1, 131 – 140 (German). · Zbl 0077.11002
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