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Iterative solution of nonlinear equations of the monotone type in Banach spaces
| Content Provider | Scilit |
|---|---|
| Author | Chidume, C. E. |
| Copyright Year | 1990 |
| Description | Let E be a real Banach space with a uniformly convex dual, and let K be a nonempty closed convex and bounded subset of E. Suppose T: K → K is a continuous monotone map. Define S: K → K by Sx = f – Tx for each x in K and define the sequence iteratively by $x_{0}$ ∈ K, $x_{n+1}$ = (1 – $C_{n})x_{n}$ + $C_{n}S_{xn}$, n ≥ 0, where is a real sequence satisfying appropriate conditions. Then, for any given f in K, the sequence converges strongly to a solution of x + Tx = f in K. Explicit error estimates are also computed. A related result deals with iterative solution of nonlinear equations of the dissipative type. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/3800A252EA2F4AC9113E4A856BCCBD5C/S0004972700028112a.pdf/div-class-title-iterative-solution-of-nonlinear-equations-of-the-monotone-type-in-banach-spaces-div.pdf |
| Ending Page | 31 |
| Page Count | 11 |
| Starting Page | 21 |
| ISSN | 00049727 |
| e-ISSN | 17551633 |
| DOI | 10.1017/s0004972700028112 |
| Journal | Bulletin of the Australian Mathematical Society |
| Issue Number | 1 |
| Volume Number | 42 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1990-08-01 |
| Access Restriction | Open |
| Subject Keyword | Bulletin of the Australian Mathematical Society Applied Mathematics Nonlinear Equation Banach Space |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
