Another control condition in an iterative method for nonexpansive mappings. (English) Zbl 1030.47036
The author proves the convergence of an iterative method to approximate a fixed point of a nonexpansive mapping in a uniformly smooth Banach space.
Reviewer: Ioan A.Rus (Cluj-Napoca)
MSC:
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47H10 | Fixed-point theorems |
| 65J15 | Numerical solutions to equations with nonlinear operators |
| 47J25 | Iterative procedures involving nonlinear operators |
References:
| [1] | DOI: 10.1007/BF01190119 · Zbl 0797.47036 · doi:10.1007/BF01190119 |
| [2] | DOI: 10.1090/S0002-9939-97-04033-1 · Zbl 0888.47034 · doi:10.1090/S0002-9939-97-04033-1 |
| [3] | Reich, Panamer. Math. J. 4 pp 23– (1994) |
| [4] | DOI: 10.1007/BF00251595 · Zbl 0148.13601 · doi:10.1007/BF00251595 |
| [5] | Lions, C.R. Acad. Sci. Paris, Sér. A 284 pp 1357– (1977) |
| [6] | DOI: 10.1090/S0002-9904-1967-11864-0 · Zbl 0177.19101 · doi:10.1090/S0002-9904-1967-11864-0 |
| [7] | DOI: 10.1016/0022-247X(80)90323-6 · Zbl 0437.47047 · doi:10.1016/0022-247X(80)90323-6 |
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