New technique for proving 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/jnaat341-796

Keywords:

Mann iteration, Ishikawa iteration, uniformly pseudocontractive, uniformly accretive map
Abstract views: 224

Abstract

We show the equivalence bewteen the convergences of Mann and Ishikawa iterations dealing with various classes of non-Lipschitzian operators.

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References

S. Ishikawa, 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

W. R. Mann, 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. and Şoltuz, Şt. M., The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitzian operators, Int. J. Math. Math. Sci., 2003, pp. 2645-2652, https://doi.org/10.1155/s0161171203211418 DOI: https://doi.org/10.1155/S0161171203211418

Rhoades, B. E. and Şoltuz, Şt. M., The equivalence of Mann and Ishikawa iteration for a Lipschitzian psi-uniformly pseudocontractive and psi-uniformly accretive maps, Tamkang J. Math., 35, pp. 235-245, 2004, https://doi.org/10.5556/j.tkjm.35.2004.204 DOI: https://doi.org/10.5556/j.tkjm.35.2004.204

Rhoades, B. E. and Şoltuz, Şt. M., The equivalence of Mann and Ishikawa iteration for ψ-uniformly pseudocontractive or ψ-uniformly accretive maps, Int. J. Math. Math. Sci., 46, pp. 2443-2452, 2004, https://doi.org/10.1155/s0161171204312020 DOI: https://doi.org/10.1155/S0161171204312020

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Published

2005-02-01

How to Cite

Şoltuz, Ştefan M. (2005). New technique for proving the equivalence of Mann and Ishikawa iterations. Rev. Anal. Numér. Théor. Approx., 34(1), 103–108. https://doi.org/10.33993/jnaat341-796

Issue

Vol. 34 No. 1 (2005)

Section

Articles

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

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