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


47H10 Fixed-point theorems
65J05 General theory of numerical analysis in abstract spaces
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[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, (), 267-273 · Zbl 0291.54056
[4] Franks, R.L; Marzec, R.P, A theorem on Mean value iterations, (), 324-326 · Zbl 0229.26005
[5] Ishikawa, S, Fixed points by a new iteration method, (), 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, (), 390-395 · Zbl 0303.47036
[8] {\scB. E. Rhoades}, Fixed point iteration using infinite matrices, III, in “Conference on Computing Fixed Points with Applications,” Academic Press, New York, to appear.
[9] {\scB. E. Rhoades}, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., to appear. · Zbl 0394.54026
[10] Zamfirescu, T, Fix point theorems in metric spaces, Arch. math., 23, 292-298, (1972) · Zbl 0239.54030
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