ITERATION PROCESSES OF ASYMPTOTICALLY PSEUDO-CONTRACTIVE MAPPINGS IN BANACH SPACES

  • Published : 2001.08.01

Abstract

Some convergence theorems of modified Ishikawa and Mann iteration processes with errors for asymptotically pseudo-contractive and asymptotically nonexpansive mappings in Banach spaces are obtained. The results presented in this paper improve and extend the corresponding results in Liu [7] and Schu [10].

Keywords

References

  1. Proc. Nat. Acad. Sci. v.54 Nonexpansive nonlinear operators in Banach spaces F. E. Browder
  2. Nonlinear Anal. TMA v.30 no.7 Some problems and results in the study of nonlinear analysis S. S. Chang
  3. Proc. Amer. Math. Soc. v.35 no.1 A fixed point theorem for asymptotically nonexpansive mappings K. Goebel;W. A. Kirk
  4. Proc. Amer. Math. Soc. v.44 Fixed points by a new iteration method S. Ishikawa
  5. Amer. Math. Monthly v.72 A fixed point theorem for mappings which do not increase distance W. A. Kirk
  6. J. Math. Anal. Appl. v.194 Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces L. S. Liu
  7. Nonlinear Anal. TMA v.26 no.11 Convergence theorems of the sequence of iterates for asymptotically demi-contractive and hemi-contractive mappings Q. H. Liu
  8. Proc. Amer. Math. Soc. v.4 Mean value methods in iteration W. R. Mann
  9. J. Math. Anal. Appl. v.56 Comments on two fixed point iterative methods B. E. Rhoades
  10. J. Math. Anal. Appl. v.158 Iterative construction of fixed points of asymptotically nonexpansive mappings J. Schu
  11. J. Math. Anal. Appl. v.167 A necessary and sufficient condition for convergence of steepest decent approximation to accretive operator equations Z. B. Xu;G. F. Roach