Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Strong Convergence Theorems for Asymptotically Nonexpansive Mappings by Hybrid Methods

  • Qin, Xiaolong (Department of Mathematics, Tianjin Polytechnic University) ;
  • Su, Yongfu (Department of Mathematics, Tianjin Polytechnic University) ;
  • Shang, Meijuan (Department of Mathematics, Tianjin Polytechnic University, Department of Mathematics, Shijiazhuang University)
  • Received : 2007.01.08
  • Published : 2008.03.31
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Abstract

In this paper, we prove two strong convergence theorems for asymptotically nonexpansive mappings in Hibert spaces by hybrid methods. Our results extend and improve the recent ones announced by Nakajo, Takahashi [K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372-379], Kim, Xu [T. H. Kim, H. K. Xu, Strong convergence of modified mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal. 64 (2006) 1140-1152], Martinez-Yanes, Xu [C. Martinez-Yanes, H. K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006) 2400-2411] and some others.

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References

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