Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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REMARKS ON APPROXIMATION OF FIXED POINTS OF STRICTLY PSEUDOCONTRACTIVE MAPPINGS

  • Kim, Tae-Hwa (Department of Applied Mathematics, Pukyong National University) ;
  • Kim, Eun-Suk (Department of Applied Mathematics, Pukyong National University)
  • Published : 2000.08.01
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Abstract

In the present paper, we first give some examples of self-mappings which are asymptoticaly nonexpansive in the intermediate, not strictly hemicontractive, but satisfy the property (H). It is then shown that the modified Mann and Ishikawa iteration processes defined by $x_{n+1}=(1-\alpha_n)x_n+\alpha_nT^nx_n\ and\ x_{n+1}=(1-\alpha_n)x_n+\alpha_nT^n[(1-\beta_n)x_n+\beta_nT^nx_n]$,respectively, converges strongly to the unique fixed point of such a self-mapping in general Banach spaces.

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References

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