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APPROXIMATING COMMON FIXED POINTS OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

  • Cho, Yeol-Je (The Research Institute of Natural Sciences and Department of Machematics Education, College of Education, Gyeongsang National Univeristy) ;
  • Kang, Jung-Im (Department of Mathematics, College of Natural Sciences Gyeongsang National University) ;
  • Zrou, Haiyun (Department of Mathematics, Shijiazhuang Mechanical Engineering College)
  • Published : 2005.11.01

Abstract

In this paper, we deal with approximations of com­mon fixed points of the iterative sequences with errors for three asymptotically nonexpansive mappings in a uniformly convex Banach space. Our results generalize and improve the corresponding results of Khan and Takahashi, Schu, Takahashi and Tamura, and others.

References

  1. S. S. Chang, Y. J. Cho, and H. Y. Zhou, Iterative Methods for Nonlinear Operator Equations in Banach Spaces, Nova Science Publishers, Inc., New York (2002)
  2. G. Das and J. P. Debata, Fixed points of quasi-nonexpansive mappings, Indian J. Pure Appl. Math. 17 (1986), 1263-1269
  3. K. Goebel and W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), no. 1, 171-174
  4. J. Gornicki, Weak convergence theorems for asymptotically nonexpansive mappings in uniformly convex Banach spaces, Comment. Math. Univ. Carolin. 30 (1989), 249-252
  5. S. H. Khan and W. Takahashi, Approximating common fixed points of two asymptotically nonexpansive mappings, Sci. Math. Jpn. 53 (2001), 143-148
  6. S. H. Khan and W. Takahashi, Iterative approximation of fixed points of two asymptotically nonexpansive mappings without compact domains, to appear in Panamer. Math. J.
  7. Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 59-59 https://doi.org/10.1090/S0002-9904-1967-11640-9
  8. J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc. 43 (1991), 153-159 https://doi.org/10.1017/S0004972700028884
  9. J. Schu, Iterative construction of fixed points of asymptotically nonexpansive mappings, J. Math. Anal. Appl. 158 (1991), 407-413 https://doi.org/10.1016/0022-247X(91)90245-U
  10. W. Takahashi and T. Tamura, Convergence theorems for a pair of nonexpansive mappings, J. Convex Anal. 5 (1995), no. 1, 45-58
  11. K. K. Tan and H. K. Xu, Approximating fixed points of nonexpansive mappings, J. Math. Anal. Appl. 178 (1993), 301-308 https://doi.org/10.1006/jmaa.1993.1309

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