# zbMATH — the first resource for mathematics

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
Full Text:
##### References:
 [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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.