×

On an application of Newton’s method to nonlinear operators with \(\omega\)-conditioned second derivative. (English) Zbl 1028.65061

Convergence of the Newton method for solving nonlinear operator equations \(F(x)=0\) in a Banach space is studied under the condition \(\|F''(x)\|\leq\omega(\|x\|)\). Here \(\omega:\mathbb R_+\cup\{0\} \mapsto \mathbb R_+\cup\{0\}\) is a continuous and monotonous function. The existence and uniqueness of a solution is established under this type of assumptions on \(F''(x)\). A nonlinear Hammerstein integral equation is used to illustrate application of the analysis.
Reviewer: Zhen Mei (Toronto)

MSC:

65J15 Numerical solutions to equations with nonlinear operators
47J25 Iterative procedures involving nonlinear operators
65R20 Numerical methods for integral equations
45G10 Other nonlinear integral equations
PDFBibTeX XMLCite