| Title:
|
Dual convergences of iteration processes for nonexpansive mappings in Banach spaces (English) |
| Author:
|
Jung, Jong Soo |
| Author:
|
Sahu, Daya Ram |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
2 |
| Year:
|
2003 |
| Pages:
|
397-404 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we establish a dual weak convergence theorem for the Ishikawa iteration process for nonexpansive mappings in a reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm, and then apply this result to study the problem of the weak convergence of the iteration process. (English) |
| Keyword:
|
Banach limit |
| Keyword:
|
dual convergence theorem |
| Keyword:
|
duality mapping |
| Keyword:
|
Ishikawa iteration process |
| Keyword:
|
nonexpansive mapping |
| MSC:
|
47H09 |
| MSC:
|
47H10 |
| MSC:
|
47J25 |
| idZBL:
|
Zbl 1030.47037 |
| idMR:
|
MR1983460 |
| . |
| Date available:
|
2009-09-24T11:02:38Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127808 |
| . |
| Reference:
|
[1] R. E. Bruck and S. Reich: Accretive operators, Banach limits and dual ergodic theorems.Bull. Acad. Polon. Sci. 29 (1981), 585–589. MR 0654218 |
| Reference:
|
[2] L. Deng: Convergence of the Ishikawa iteration process for nonexpansive mappings.J. Math. Anal. Appl. 199 (1996), 769–775. Zbl 0856.47041, MR 1386604 |
| Reference:
|
[3] K. Goebel and S. Reich: Uniform Convexity, Hyperbolic Geometry and Nonexpansive Mappings.Marcel Dekker, New York and Basel, 1984. MR 0744194 |
| Reference:
|
[4] S. Ishikawa: Fixed point by a new iteration method.Proc. Amer. Math. Soc. 44 (1974), 147–150. MR 0336469, 10.1090/S0002-9939-1974-0336469-5 |
| Reference:
|
[5] K. S. Ha and J. S. Jung: Strong convergence theorems for accretive operators in Banach spaces.J. Math. Anal. Appl. 104 (1990), 330–339. MR 1050208, 10.1016/0022-247X(90)90351-F |
| Reference:
|
[6] G. G. Lorentz: A contribution to the theory of divergent series.Acta Math. 80 (1948), 167–190. MR 0027868, 10.1007/BF02393648 |
| Reference:
|
[7] W. R. Mann: Mean value methods in iteration.Proc. Amer. Math. Soc. 4 (1953), 506–510. Zbl 0050.11603, MR 0054846, 10.1090/S0002-9939-1953-0054846-3 |
| Reference:
|
[8] S. Reich: Weak convergence theorem for nonexpansive mappings in Banach spaces.J. Math. Anal. Appl. 67 (1979), 274–276. MR 0528688, 10.1016/0022-247X(79)90024-6 |
| Reference:
|
[9] S. Reich: Product formulas, nonlinear semigroups and accretive operators.J. Functional Analysis 36 (1980), 147–168. Zbl 0437.47048, MR 0569251, 10.1016/0022-1236(80)90097-X |
| Reference:
|
[10] K. K. Tan and H. K. Xu: Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process.J. Math. Anal. Appl. 178 (1993), 301–308. MR 1238879, 10.1006/jmaa.1993.1309 |
| . |
