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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.

65H05 Numerical computation of solutions to single equations
Full Text: DOI
[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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