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A fixed point theorem for mappings with a nonexpansive iterate. (English) Zbl 0213.41303

MSC:
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
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[1] L. P. Belluce and W. A. Kirk, Fixed-point theorems for certain classes of nonexpansive mappings, Proc. Amer. Math. Soc. 20 (1969), 141 – 146. · Zbl 0165.16801
[2] M. S. Brodskiĭ and D. P. Mil\(^{\prime}\)man, On the center of a convex set, Doklady Akad. Nauk SSSR (N.S.) 59 (1948), 837 – 840 (Russian).
[3] Felix E. Browder, Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1041 – 1044. · Zbl 0128.35801
[4] K. Goebel, Convexivity of balls and fixed-point theorems for mappings with nonexpansive square, Compositio Math. 22 (1970), 269 – 274. · Zbl 0202.12802
[5] Dietrich Göhde, Zum Prinzip der kontraktiven Abbildung, Math. Nachr. 30 (1965), 251 – 258 (German). · Zbl 0127.08005
[6] W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004 – 1006. · Zbl 0141.32402
[7] Victor L. Klee Jr., Convex bodies and periodic homeomorphisms in Hilbert space, Trans. Amer. Math. Soc. 74 (1953), 10 – 43. · Zbl 0050.33202
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