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An example concerning fixed points. (English) Zbl 0314.47031

MSC:
47H10Fixed point theorems for nonlinear operators on topological linear spaces
46C05Hilbert and pre-Hilbert spaces: geometry and topology
References:
[1]F. E. Browder,Non expansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U.S.A.54 (1965), 1041–1044. · Zbl 0128.35801 · doi:10.1073/pnas.54.4.1041
[2]S. Kaniel,Construction of a fixed point for contractions in Banach spaces, Israel J. Math.,9 (1971), 535–540. · Zbl 0222.47022 · doi:10.1007/BF02771468
[3]W. A. Kirk,A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly72 (1965), 1004–1006. · Zbl 0141.32402 · doi:10.2307/2313345
[4]M. D. Kirzbraun,Über die zusammenziehenden und Lipshitzschen Transformationen, Fund. Math.22 (1934), 77–108.
[5]M. A. Krasnoselski,Two remarks on the method of successive approximation, Uspehi Mat. Nauk10 (1955), 123–127.
[6]Z. Opial,Weak convergence of the successive approximations for non expansive mappings in Banach spaces, Bull. Amer. Math. Soc.73 (1967), 591–597. · Zbl 0179.19902 · doi:10.1090/S0002-9904-1967-11761-0