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Comments on two fixed point iteration methods. (English) Zbl 0353.47029


MSC:

47H10 Fixed-point theorems
65J05 General theory of numerical analysis in abstract spaces
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References:

[1] Browder, F. E.; Petryshyn, W. V., Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl., 20, 65-73 (1967) · Zbl 0153.45701
[2] Dotson, W. G., On the Mann iterative process, Trans. Amer. Math. Soc., 149, 65-73 (1970) · Zbl 0203.14801
[3] Ćirić, L. B., A generalization of Banach’s contraction principle, (Proc. Amer. Math. Soc., 45 (1974)), 267-273 · Zbl 0291.54056
[4] Franks, R. L.; Marzec, R. P., A theorem on mean value iterations, (Proc. Amer. Math. Soc., 30 (1971)), 324-326 · Zbl 0229.26005
[5] Ishikawa, S., Fixed points by a new iteration method, (Proc. Amer. Math. Soc., 44 (1974)), 147-150 · Zbl 0286.47036
[6] Rhoades, B. E., Fixed point iterations using infinite matrices, Trans. Amer. Math. Soc., 196, 161-176 (1974) · Zbl 0285.47038
[7] Rhoades, B. E., Fixed point iterations using infinite matrices, II, (Constructive and Computational Methods for Differential and Integral Equations. Constructive and Computational Methods for Differential and Integral Equations, Springer-Verlag Lecture Notes Series, Vol. 430 (1974), Springer-Verlag: Springer-Verlag New York/Berlin), 390-395 · Zbl 0303.47036
[10] Zamfirescu, T., Fix point theorems in metric spaces, Arch. Math., 23, 292-298 (1972) · Zbl 0239.54030
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