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Construction of fixed points of a class of nonlinear mappings. (English) Zbl 0261.47037


MSC:

47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
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References:

[1] Browder, F. E., Nonexpansive nonlinear operators in a Banach space, (Proc. Nat. Acad. Sci., 54 (1965)), 1041-1044 · Zbl 0128.35801
[2] Browder, F. E.; Petryshyn, W. V., The solution by iteration of nonlinear functional equations in Banach spaces, Bull. Amer. Math. Soc., 72, 571-575 (1966) · Zbl 0138.08202
[3] Danes, J., Some fixed point theorems in metric and Banach spaces, Comment. Math. Univ. Carolinae, 12, 37-52 (1971) · Zbl 0224.47032
[4] Edelstein, M., A remark on a theorem of M.A. Krasnoselskii, Amer. Math. Monthly, 73, 509-510 (1966) · Zbl 0138.39901
[5] Gohde, D., Zum Prinzip der kontraktiven Abbildung, Math. Nach., 30, 251-258 (1965) · Zbl 0127.08005
[6] Kannan, R., Some results on fixed points, Bull. Calcutta Math. Soc., 60, 71-76 (1968) · Zbl 0209.27104
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[9] Kannan, R., Some results on fixed points—IV, Fund. Math., LXXIV, 181-187 (1972) · Zbl 0257.54044
[10] R. KannanProc. Amer. Math. Soc.; R. KannanProc. Amer. Math. Soc. · Zbl 0265.47038
[11] Kirk, W. A., A fixed point theorem for mappings which do not increase distances, Amer. Math. Montly, 72, 1004-1006 (1965) · Zbl 0141.32402
[12] Kirk, W. A., On successive approximations for nonexpansive mappings in Banach spaces, Glasgow Math. J., 12, 6-9 (1971) · Zbl 0223.47024
[13] Krasnoselskii, M. A., Two remarks about the method of successive approximations, Uspehi. Math. Nauk, 10, 123-127 (1955)
[14] Petryshyn, W. V., Construction of fixed points for demicompact mappings in Hilbert space, J. of Math. Anal. Appl., 14, 276-284 (1966) · Zbl 0138.39802
[15] Reich, S., Kannan’s fixed point theorem, Boll. Unione. Math. Italy, 4, 1-11 (1971) · Zbl 0219.54042
[16] Schaefer, H., Über die Methode suksessiver Approximation, Jber. Deutsch. Math.-Verein, 59, 131-140 (1957)
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