Abstract
We show the equivalence bewteen the convergences of Mann andIshikawa iterations dealing with various classes of non-Lipschitzian operators.
Authors
Stefan M. Soltuz
Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy, Romania
Keywords
Mann iteration; Ishikawa iteration; uniformly pseudocontractive; uniformly accretive map
Paper coordinates
Ş.M. Şoltuz, New technique for proving the equivalence of Mann and Ishikawa iterations, Rev. Anal. Numer. Theor. Approx., 34 (2005) no. 1, 103-108.
About this paper
Journal
Rev. Anal. Numer. Theor. Approx.
Publisher Name
Romanian Academy
Print ISSN
2457-6794
Online ISSN
2501-059X
google scholar link
[1] S.Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc.,44,pp. 147–150, 1974.
[2] W. R.Mann, Mean value in iteration, Proc. Amer. Math. Soc.,4, pp. 506–510, 1953.
[3] Rhoades, B. E. and Soltuz, S ̧t. M., The equivalence of Mann iteration and Ishikawaiteration for non-Lipschitzian operators,Int. J. Math. Math. Sci.,2003, pp. 2645–2652.
[4] Rhoades, B. E. and Soltuz, S ̧t. 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.
[5] Rhoades, B. E. and Soltuz, S ̧t. M., The equivalence of Mann and Ishikawa iterationforψ-uniformly pseudocontractive orψ-uniformly accretive maps,Int. J. Math. Math.Sci.,46, pp. 2443–2452, 2004.Received by the editors: April 15, 2005.
[2] W. R.Mann, Mean value in iteration, Proc. Amer. Math. Soc.,4, pp. 506–510, 1953.
[3] Rhoades, B. E. and Soltuz, S ̧t. M., The equivalence of Mann iteration and Ishikawaiteration for non-Lipschitzian operators,Int. J. Math. Math. Sci.,2003, pp. 2645–2652.
[4] Rhoades, B. E. and Soltuz, S ̧t. 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.
[5] Rhoades, B. E. and Soltuz, S ̧t. M., The equivalence of Mann and Ishikawa iterationforψ-uniformly pseudocontractive orψ-uniformly accretive maps,Int. J. Math. Math.Sci.,46, pp. 2443–2452, 2004.Received by the editors: April 15, 2005.