Remarks about a paper dealing with the equivalence of Mann and Ishikawa iterations

Authors

  • Ştefan M Şoltuz Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy, Romania

DOI:

https://doi.org/10.33993/jnaat332-784

Keywords:

Mann iteration, Ishikawa iteration
Abstract views: 178

Abstract

We give an affirmative answer to the following question: are Mann and Ishikawa iterations equivalent under the assumptions that \(\lim_{n\rightarrow\infty }\alpha_{n}\neq0\;\) and \(\lim_{n\rightarrow\infty}\beta_{n}\neq0\)?

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References

Ishikawa, S., Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44, pp. 147-150, 1974, https://doi.org/10.1090/S0002-9939-1974-0336469-5. DOI: https://doi.org/10.1090/S0002-9939-1974-0336469-5

Liu, Liwei, Approximation of fixed points of a strictly pseudocontractive mapping, Proc. Amer. Math. Soc., 125, pp. 1363-1366, 1997, https://www.jstor.org/stable/2162078. DOI: https://doi.org/10.1090/S0002-9939-97-03858-6

Mann, W.R., Mean value in iteration, Proc. Amer. Math. Soc., 4, pp. 506-510, 1953, https://doi.org/10.2307/2032162. DOI: https://doi.org/10.1090/S0002-9939-1953-0054846-3

Rhoades, B. E., Şoltuz, Ş. M., On the equivalence of Mann and Ishikawa iteration methods, Int. J. Math. Math. Sci., 2003, pp. 451-459, 2003. DOI: https://doi.org/10.1155/S0161171203110198

Sastry, K. P. R., Babu, G. V. R., Approximation of fixed points of strictly pseudocontractive mappings on arbitrary closed convex sets in a Banach space, Proc. Amer. Math. Soc., 128, pp. 2907-2909, 2000, https://doi.org/10.1090/S0002-9939-00-05362-4. DOI: https://doi.org/10.1090/S0002-9939-00-05362-4

Zeng, Luchuan, Ishikawa iterative procedure points of strictly pseudocontractive mappings, Appl. Math. J. Chinese Univ. Ser. B, 18, pp. 283-286, 2003. DOI: https://doi.org/10.1007/s11766-003-0052-z

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Published

2004-08-01

How to Cite

Şoltuz, Ştefan M. (2004). Remarks about a paper dealing with the equivalence of Mann and Ishikawa iterations. Rev. Anal. Numér. Théor. Approx., 33(2), 247–249. https://doi.org/10.33993/jnaat332-784

Issue

Vol. 33 No. 2 (2004)

Section

Articles

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Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

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