Name
Abstract | ||
|---|---|---|
Ostrowski provided the sharp sufficient condition ρ(F′(x∗))<1 for x∗ to be an attraction point, for a nonlinear mapping differentiable at a fixed point x∗[1]. This result provides no estimate for the size of the attraction ball. Recently, Cătinaş [2] provided such an estimate in terms of ‖F′(x∗)‖<1 in a Hölder continuity setting. We show that the results by Cătinaş remain valid in a weaker setting by simply replacing the Hölder by the center-Hölder continuity assumption. The radius of convergence of Picard’s iteration is extended, which allows a wider choice of initial guesses. Moreover the estimates of the distances ‖x0−x∗‖ are more precise, which lead to the computation of fewer iterates to achieve a desired accuracy. We also provide examples where our results apply, whereas those by Cătinaş [2] do not, or where our results are better. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.aml.2009.11.007 | Applied Mathematics Letters |
Keywords | Field | DocType |
Fixed points,Attraction points,Attraction ball,Center-Hölder continuity | Convergence (routing),Mathematical optimization,Nonlinear system,Radius of convergence,Mathematical analysis,Differentiable function,Hölder condition,Fixed point,Iterated function,Mathematics,Computation | Journal |
Volume | Issue | ISSN |
23 | 4 | 0893-9659 |
Citations | PageRank | References |
2 | 0.46 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jinhai Chen | 1 | 13 | 3.55 |
| Ioannis K. Argyros | 2 | 326 | 77.73 |