On the boundedness of the associated sequence of Mann iteration for several operator classes with applications

Authors

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

DOI:

https://doi.org/10.33993/jnaat342-808

Keywords:

Ishikawa-Mann iteration, associated Mann sequence
Abstract views: 198

Abstract

We prove that the associated sequence of Mann iteration is decreasing and hence bounded provided that the operator satisfies minimal assumptions. In particular we obtain for a nonexpansive operator that the associated sequence of Ishikawa iteration is decreasing for a nonexpansive operator. Applications to the convergence of Mann iteration are given.

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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

Mann, W.E., Mean value in iteration, Proc. Amer. Math. Soc., 4, pp. 506-510, 1953, https://doi.org/10.1090/s0002-9939-1953-0054846-3 DOI: https://doi.org/10.1090/S0002-9939-1953-0054846-3

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

Weng, X., Fixed point iteration for local strictly pseudocontractive mapping, Proc. Amer. Math. Soc., 113, pp. 727-731, 1991, https://doi.org/10.1090/s0002-9939-1991-1086345-8 DOI: https://doi.org/10.1090/S0002-9939-1991-1086345-8

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Published

2005-08-01

How to Cite

Şoltuz, Ştefan M. (2005). On the boundedness of the associated sequence of Mann iteration for several operator classes with applications. Rev. Anal. Numér. Théor. Approx., 34(2), 227–232. https://doi.org/10.33993/jnaat342-808

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Articles