Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings

Proceedings of the American Mathematical Society

Volumn 129, Issue 3, 2001, Pages 845-853

  Chang, S S ^a  

^a SICHUAN UNIVERSITY   (China)

Author keywords

Asymptotically nonexpansive mapping; Asymptotically pseudo contractive mapping; Fixed point; Modified isikawa iterative sequence with errors; Modified mann iterative sequence with error

Indexed keywords

EID: 0004316906     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-00-05988-8     Document Type: Article

References (12)

1. F. E. Browder, Nonexpansive nonlinear operators in Banach spaces, Proc. Natl. Acad. Sci. USA, 54 (1965), 1041-1044. MR 32:4574
2. Shih-sen Chang, Some problems and results in the study of nonlinear analysis, Nonlinear Anal. TMA, 30 (1997), 4197-4208. MR 99a:47089
3. Shih-sen Chang, J. Y. Park and I. H. Jung, Some results on convergence of iterative methods for accretive and pseudo-contractive type mappings in Banach spaces, (submitted).
4. Shih-sen Chang, J. Y. Park, Y. J. Cho and I. H. Jung, Iterative approximations of asymptotically pseudo-contractive mappings in Banach spaces, (submitted).
5. K. Goebel and W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35 (1) (1972), 171-174. MR 45:7552
6. W. A. Kirk, A fixed point theorem for mappings which do not increase distance, Amer. Math. Monthly, 72 (1965), 1004-1006. MR 32:6436
7. Q. H. Liu, Convergence theorems of the sequence of iterates for asymptotically demi-contractive and hemi-contractive mappings, Nonlinear Anal. TMA, 26 (11) (1996), 1835-1842. MR 97d:47069
8. B. E. Rhoades, Comments on two fixed point iterative methods, J. Math. Anal. Appl., 56 (1976), 741-750. MR 55:3885
9. J. Schu, Iterative construction of fixed points of asymptotically nonexpansive mappings, J. Math. Anal. Appl., 158 (1991), 407-413. MR 92d:47072
10. H. K. Xu, Inequalities in Banach spaces with applications, Nonlinear Anal. TMA, 16 (12) (1991), 1127-1138. MR 92e:47126
11. H. K. Xu, Existence and convergence for fixed points of mapping of asymptotically nonexpansive type, Nonlinear Anal. TMA, 16 (12) (1991), 1139-1146. MR 92h:47089
12. Z. B. Xu and G. F. Roach, A necessary and sufficient condition for convergence of steepest descent approximation to accretive operator equations, J. Math. Anal. Appl., 167 (1992), 340-354. MR 93e:47086