Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지

WEAK CONVERGENCE TO COMMON FIXED POINTS OF COUNTABLE NONEXPANSIVE MAPPINGS AND ITS APPLICATIONS

  • Kimura, Yasunori (Institute of Economic Research Hitotsubashi University) ;
  • Takahashi, Wataru (Department of Mathematical and Computing Sciences Tokyo Institute of Technology)
  • Published : 2001.11.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we introduce an iteration generated by countable nonexpansive mappings and prove a weak convergence theorem which is connected with the feasibility problem. This result is used to solve the problem of finding a solution of the countable convex inequality system and the problem of finding a common fixed point for a commuting countable family of nonexpansive mappings.

Keywords

References

  1. Proc. Sympos. Pure Math. v.18 no.2 Nonlinear operators and nonlinear equations of evolutions in Banach spaces F. E. Browder
  2. Trans. Amer. Math. Soc. v.179 Properties of fixed-point sets of nonexpansive mappings in Banach spaces R. E. Bruck
  3. Pacific J. Math. v.53 A common fixed-point theorem for a commuting family of nonexpansive mappings R. E. Bruck
  4. J. Math. Anal. Appl. v.155 Image recovery by convex combinations of projections G. Crombez
  5. Indian J. Pure Appl. Math. v.17 Fixed points of quasi-nonexpansive mappings G. Das;J. P. Debeta
  6. Nonlinear Anal. v.18 Unrestricted iterations of nonexpensive mappings in Hillbert space J. M. Dye;S. Reich
  7. Proc. Amer. Math. Soc. v.44 Fixed points by a new iteration method S. Ishikawa
  8. Topol. Methods Nonlinear Anal. v.2 Image recovery by convex combinations for sunny nonexpansive retractions S. Kitahara;W. Takahashi
  9. Amer. Math. Monthly v.72 A fixed point theorem for mappings which do not increase distances W. A. Kirk
  10. Bull. Amer. Math. Soc. v.73 Weak convergence of the sequence of successive approximations for nonexpansive mappings Z. Opial
  11. J. Math. Anal. Appl. v.67 Weak convergence theorems for nonexpansive mappings in Banach spaces S. Reich
  12. Bull. Austral. Math. Soc. v.43 Weak and strongs convergence to fixed points of asymptotically nonexpansive mappings J. Schu
  13. Ann. Univ. Mariae Curie-Sklodwska v.51 Weak and strong convergence theorems for families of nonexpansive mappings and their applications W. Takahashi
  14. Math. Japon. v.48 Approximating fixed points of nonexpansive mappings in Banach spaces W. Takahashi;G. E. Kim
  15. Math. Comput. Modelling v.32 Convergence theorems for nonexpansive mappings and feasibility problems W. Takahashi;K. Shimoji