The equivalence between T-stabilities of Krasnoselskij and Ishikawa iterations

Authors

  • Ştefan M. Şoltuz Universidad de los Andes, Colombia and Tiberiu Popoviciu Institute of Numerical Analysis, Romania

DOI:

https://doi.org/10.33993/jnaat371-880

Keywords:

Krasnoselskij iteration, Ishikawa iteration, Picard-Banach iteration
Abstract views: 196

Abstract

We prove the equivalence between the \(T\)-stabilities of Krasnoselskij and Ishikawa iterations; a consequence is the equivalence with the \(T\)-stability of Picard-Banach iteration.

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References

Harder, A.M. and Hicks, T., Stability results for fixed point iteration procedures, Math. Japonica, 33, pp. 693-706, 1988.

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

Krasnoselskij, M.A., Two remarks on the method of succesive approximations, Uspehi Mat. Nauk., 10, pp. 123-127, 1955.

Mann, W.R., Mean value methods 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. and Şoltuz, Ş.M., The equivalence between the T-stabilities of Mann and Ishikawa iterations, J. Math. Anal. Appl., 318, pp. 472-475, 2006, https://doi.org/10.1016/j.jmaa.2005.05.066 DOI: https://doi.org/10.1016/j.jmaa.2005.05.066

Şoltuz, Ş.M., The equivalence between the T-stabilities of Picard-Banach and Mann-Ishikawa iterations, Appl. Math. E-Notes, 8, pp. 109 -114, 2008.

Şoltuz, Ş.M., The equivalence between T-stabilities of the Krasnoselskij and the Mann iterations, Fixed Point Theory and Applications, 2007, Article ID 60732. DOI: https://doi.org/10.1155/2007/60732

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Published

2008-02-01

How to Cite

Şoltuz, Ştefan M. (2008). The equivalence between T-stabilities of Krasnoselskij and Ishikawa iterations. Rev. Anal. Numér. Théor. Approx., 37(1), 99–104. https://doi.org/10.33993/jnaat371-880

Issue

Vol. 37 No. 1 (2008)

Section

Articles

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

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