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Properties of fixed-point sets of nonexpansive mappings in Banach spaces. (English) Zbl 0265.47043

MSC:
47H10 Fixed-point theorems
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[1] L. P. Belluce and W. A. Kirk, Fixed-point theorems for families of contraction mappings, Pacific J. Math. 18 (1966), 213 – 217. · Zbl 0149.10701
[2] L. P. Belluce and W. A. Kirk, Nonexpansive mappings and fixed-points in Banach spaces, Illinois J. Math. 11 (1967), 474 – 479. · Zbl 0149.10702
[3] M. S. Brodskiń≠ and D. P. Mil\(^{\prime}\)man, On the center of a convex set, Doklady Akad. Nauk SSSR (N.S.) 59 (1948), 837 – 840 (Russian).
[4] Ronald E. Bruck Jr., Nonexpansive retracts of Banach spaces, Bull. Amer. Math. Soc. 76 (1970), 384 – 386. · Zbl 0224.47034
[5] Ralph DeMarr, Common fixed points for commuting contraction mappings, Pacific J. Math. 13 (1963), 1139 – 1141. · Zbl 0191.14901
[6] Michael Edelstein, On nonexpansive mappings, Proc. Amer. Math. Soc. 15 (1964), 689 – 695. · Zbl 0124.16004
[7] W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004 – 1006. · Zbl 0141.32402 · doi:10.2307/2313345 · doi.org
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