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On the rate of convergence of Mann, Ishikawa, Noor and SP-iterations for continuous functions on an arbitrary interval. (English) Zbl 1215.65095
The authors introduce a new iterative method to find a fixed point of a continuous function on an interval. Its convergence is characterized and shown to be faster than that of three other known methods.

MSC:
65H05 Numerical computation of solutions to single equations
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References:
[1] Mann, W.R., Mean value methods in iteration, Proc. amer. math. soc., 4, 506-510, (1953) · Zbl 0050.11603
[2] Ishikawa, S., Fixed points by a new iteration method, Proc. amer. math. soc., 44, 147-150, (1974) · Zbl 0286.47036
[3] Noor, M.A., New approximation schemes for general variational inequalities, J. math. anal. appl., 251, 217-229, (2000) · Zbl 0964.49007
[4] Rhoades, B.E., Comments on two fixed point iteration methods, J. math. anal. appl., 56, 741-750, (1976) · Zbl 0353.47029
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[6] Qing, Y.; Qihou, L., The necessary and sufficient condition for the convergence of Ishikawa iteration on an arbitrary interval, J. math. anal. appl., 323, 1383-1386, (2006) · Zbl 1101.47056
[7] Soltuz, S.M., The equivalence of Picard, Mann and Ishikawa iterations dealing with quasi-contractive operators, Math. commun., 10, 81-88, (2005) · Zbl 1089.47051
[8] Babu, G.V.; Prasad, K.N., Mann iteration converges faster than Ishikawa iteration for the class of Zamfirescu operators, Fixed point theory appl., 49615, 1-6, (2006), Article ID · Zbl 1106.47053
[9] Qing, Y.; Rhoades, B.E., Comments on the rate of convergence between Mann and Ishikawa iterations applied to Zamfirescu operators, Fixed point theory appl., 387504, 1-3, (2008), Article ID · Zbl 1203.47076
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