Name
Abstract | ||
|---|---|---|
The Mann iterations for nonexpansive mappings have only weak convergence even in a Hilbert space H. In order to overcome this weakness, Nakajo and Takahashi proposed the hybrid method for Mann’s iteration process:x0∈Cchosen arbitrarily,yn=αnxn+(1-αn)Txn,Cn=z∈C:‖yn-z‖⩽‖xn-z‖,Qn=z∈C:〈x0-xn,z-xn〉⩽0,xn+1=PCn∩Qnx0,n=0,1,2,…,where C is a nonempty closed convex subset of H, T : C→C is a nonexpansive mapping and PK is the metric projection from H onto a closed convex subset K of H. However, it is difficult to realize this iteration process in actual computing programs because the specific expression of PCn∩Qnx0 cannot be got, in general. In the case where C=H, we obtain the specific expression of PCn∩Qnx0 and thus the hybrid method for Mann’s iteration process can be realized easily. Numerical results show advantages of our result. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.amc.2010.10.039 | Applied Mathematics and Computation |
Keywords | Field | DocType |
Nonexpansive mapping,Strong convergence,Weak convergence,Hybrid method,Metric projection,Fixed point,Mann’s iteration | Hilbert space,Discrete mathematics,Mathematical optimization,Weak convergence,Mathematical analysis,Regular polygon,Metric projection,Fixed point,Mathematics,Iteration process | Journal |
Volume | Issue | ISSN |
217 | 8 | 0096-3003 |
Citations | PageRank | References |
6 | 0.85 | 2 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Songnian He | 1 | 42 | 8.08 |
| Caiping Yang | 2 | 6 | 0.85 |
| Peichao Duan | 3 | 7 | 1.96 |