Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ITERATIVE APPROXIMATION OF FIXED POINTS FOR φ-HEMICONTRACTIVE OPERATORS IN BANACH SPACES

  • Liu, Zeqing (Department of Mathematics Liaoning Normal University) ;
  • An, Zhefu (Department of Mathematics Liaoning Normal University) ;
  • Li, Yanjuan (Shenyang University) ;
  • Kang, Shin-Min (Department of Mathematics and RINS Gyeongsang University)
  • Published : 2004.01.01
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Abstract

Suppose that X is a real Banach space, K is a nonempty closed convex subset of X and T : $K\;\rightarrow\;K$ is a uniformly continuous ${\phi}$-hemicontractive operator or a Lipschitz ${\phi}-hemicontractive$ operator. In this paper we prove that under certain conditions the three-step iteration methods with errors converge strongly to the unique fixed point of T. Our results extend the corresponding results of Chang [1], Chang et a1. [2], Chidume [3]-[7], Chidume and Osilike [9], Deng [10], Liu and Kang [13], [14], Osilike [15], [16] and Tan and Xu [17].

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References

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