Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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STRONG CONVERGENCE OF MONOTONE CQ ITERATIVE PROCESS FOR ASYMPTOTICALLY STRICT PSEUDO-CONTRACTIVE MAPPINGS

  • Zhang, Hong (Department of Mathematics, Tianjin Polytechnic university) ;
  • Su, Yongfu (Department of Mathematics, Tianjin Polytechnic university) ;
  • Li, Mengqin (Department of Mathematics, Tianjin Polytechnic university)
  • Published : 2009.05.31
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Abstract

T.H. Kim, H.K. Xu, [Convergence of the modified Mann's iteration method for asymptotically strict pseudo-contractions, Nonlinear Anal.(2007),doi:l0.l016/j.na.2007.02.029.] proved the strong convergence for asymptotically strict pseudo-contractions by the classical CQ iterative method. In this paper, we apply the monotone CQ iterative method to modify the classical CQ iterative method of T.H. Kim, H.K. Xu, and to obtain the strong convergence theorems for asymptotically strict pseudo-contractions. In the proved process of this paper, Cauchy sequences method is used, so we complete the proof without using the demi-closedness principle, Opial's condition or others about weak topological technologies. In addition, we use a ingenious technology to avoid defining that F(T) is bounded. On the other hand, we relax the restriction on the control sequence of iterative scheme.

Keywords

References

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