The equivalence between the T-stabilities of modified Mann-Ishikawa and Mann-Ishikawa iterations

Authors

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

Keywords:

(modified) Mann iteration, (modified) Ishikawa iteration, \(T\)-stability

Abstract

We show that all \(T\)-stabilities of Mann-Ishikawa iterations and modified Mann-Ishikawa iterations are equivalent.

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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

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

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

Rhoades, B.E., Şoltuz, Ştefan 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

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Published

2006-08-01

How to Cite

Şoltuz, Ştefan M. (2006). The equivalence between the T-stabilities of modified Mann-Ishikawa and Mann-Ishikawa iterations. Rev. Anal. Numér. Théor. Approx., 35(2), 221–224. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2006-vol35-no2-art10

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