Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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MONOTONE CQ ALGORITHM FOR WEAK RELATIVELY NONEXPANSIVE MAPPINGS AND MAXIMAL MONOTONE OPERATORS IN BANACH SPACES

  • Kang, Jinlong (Department of Mathematics, Tianjin Polytechnic University) ;
  • Su, Yongfu (Department of Mathematics, Tianjin Polytechnic University) ;
  • Zhang, Xin (Department of Mathematics, Tianjin Polytechnic University)
  • Received : 2010.05.10
  • Accepted : 2010.06.05
  • Published : 2011.01.30
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Abstract

The purpose of this article is to prove strong convergence theorems for weak relatively nonexpansive mapping which is firstly presented in this article. In order to get the strong convergence theorems for weak relatively nonexpansive mapping, the monotone CQ iteration method is presented and is used to approximate the fixed point of weak relatively nonexpansive mapping, therefore this article apply above results to prove the strong convergence theorems of zero point for maximal monotone operators in Banach spaces. Noting that, the CQ iteration method can be used for relatively nonexpansive mapping but it can not be used for weak relatively nonexpansive mapping. However, the monotone CQ method can be used for weak relatively nonexpansive mapping. The results of this paper modify and improve the results of S.Matsushita and W.Takahashi, and some others.

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References

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