| Title:
|
Weak and strong convergence theorems of common fixed points for a pair of nonexpansive and asymptotically nonexpansive mappings (English) |
| Author:
|
Liu, Zeqing |
| Author:
|
Agarwal, Ravi P. |
| Author:
|
Feng, Chi |
| Author:
|
Kang, Shin Min |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
44 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
83-96 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The purpose of this paper is to establish some weak and strong convergence theorems of modified three-step iteration methods with errors with respect to a pair of nonexpansive and asymptotically nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper generalize, improve and unify a few results due to Chang [1], Liu and Kang [5], Osilike and Aniagbosor [7], Rhoades [8] and Schu [9], [10] and others. An example is included to demonstrate that our results are sharp. (English) |
| Keyword:
|
nonexpansive mappings |
| Keyword:
|
asymptotically nonexpansive mappings |
| Keyword:
|
common fixed points |
| Keyword:
|
modified three-step iteration methods with errors with respect to a pair of mappings |
| MSC:
|
47H05 |
| MSC:
|
47H09 |
| MSC:
|
47H10 |
| MSC:
|
47H15 |
| MSC:
|
47J25 |
| idZBL:
|
Zbl 1099.47057 |
| idMR:
|
MR2218570 |
| . |
| Date available:
|
2009-08-21T06:50:24Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133379 |
| . |
| Reference:
|
[1] Chang S. S.: On the approximation problem of fixed points for asymptotically nonexpansive mappings.Indian J. Pure Appl. Math. 32 (2001), 1297–1307. Zbl 1034.47039 |
| Reference:
|
[2] Chang S. S.: Some problems and results in the study of nonlinear analysis.Nonlinear Anal. TMA 30 (1997), 4197–4208. Zbl 0901.47036 |
| Reference:
|
[3] Goebel K., Kirk W. A.: A fixed point theorem for asymptotically nonexpansive mappings.Proc. Amer. Math. Soc. 35 (1972), 171–174. Zbl 0256.47045 |
| Reference:
|
[4] Gornicki J.: Weak convergence theorems for asymptotically nonexpansive mappings in uniformly convex Banach spaces.Comment. Math. Univ. Carolina 30 (1989), 249–252. Zbl 0686.47045 |
| Reference:
|
[5] Liu Z., Kang S. M.: Weak and strong convergence for fixed points of asymptotically nonexpansive mappings.Acta. Math. Sinica 20 (2004), 1009–1018. |
| Reference:
|
[6] Opial Z.: Weak convergence of the sequence of successive approximations for nonexpansive mappings.Bull. Amer. Math. Soc. 73 (1967), 591–597. Zbl 0179.19902 |
| Reference:
|
[7] Osilike M. O., Aniagbosor S. C.: Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings.Math. Comput. Modelling 32 (2000), 1181–1191. Zbl 0971.47038 |
| Reference:
|
[8] Rhoades B. E.: Fixed point iteration for certain nonlinear mappings.J. Math. Anal. Appl. 183 (1994), 118–120. |
| Reference:
|
[9] Schu J.: Iterative construction of fixed points of asymptotically nonexpansive mappings.J. Math. Anal. Appl. 158 (1991), 407–413. Zbl 0734.47036 |
| Reference:
|
[10] Schu J.: Weak and strong convergence of fixed points of asymptotically nonexpansive mappings.Bull. Austral. Math. Soc. 43 (1991), 153–159. |
| Reference:
|
[11] Xu H. K.: Inequalities in Banach spaces with applications.Nonlinear Anal. TMA 16 (1991), 1127–1138. Zbl 0757.46033 |
| . |
