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An example concerning fixed points. (English) Zbl 0314.47031

47H10Fixed-point theorems for nonlinear operators on topological linear spaces
46C05Hilbert and pre-Hilbert spaces: geometry and topology
Full Text: DOI
[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. · Zbl 0009.03904
[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