Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ALMOST STABILITY OF THE MANN ITERATION METHOD WITH ERRORS FOR STRICTLY HEMI-CONTRACTIVE OPERATORS IN SMOOTH BANACH SPACES

  • Liu, Z. (Department of Mathematics Liaoning Normal University) ;
  • Kang, S.M. (Department of Mathematics Gyeongsang National University) ;
  • Shim, S.H. (Department of Mathematics Gyeongsang National University)
  • Published : 2003.01.01
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Abstract

Let K be a nonempty closed bounded convex subset of an arbitrary smooth Banach space X and T : KlongrightarrowK be a strictly hemi-contractive operator. Under some conditions we obtain that the Mann iteration method with errors both converges strongly to a unique fixed point of T and is almost T-stable on K. The results presented in this paper generalize the corresponding results in [l]-[7], [20] and others.

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References

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  2. The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuousφ-strongly accretive operators in uniformly smooth Banach spaces vol.2006, 2006, https://doi.org/10.1155/IJMMS/2006/69542
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