Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON THE ON THE CONVERGENCE BETWEEN THE MANN ITERATION AND ISHIKAWA ITERATION FOR THE GENERALIZED LIPSCHITZIAN AND Φ-STRONGLY PSEUDOCONTRACTIVE MAPPINGS

  • Xue, Zhiqun
  • Published : 2008.11.30

Abstract

In this paper, we prove that the equivalence between the convergence of Mann and Ishikawa iterations for the generalized Lipschitzian and $\Phi$-strongly pseudocontractive mappings in real uniformly smooth Banach spaces. Our results significantly generalize the recent known results of [B. E. Rhoades and S. M. Soltuz, The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitz operators, Int. J. Math. Math. Sci. 42 (2003), 2645.2651].

Keywords

Ishikawa iteration;Mann iteration;$\Phi$-strongly pseudocontractive maps;generalized Lipschitz maps;uniformly smooth Banach spaces

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References

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