Ezquerro, J. A.; Hernández, M. A. On an application of Newton’s method to nonlinear operators with \(\omega\)-conditioned second derivative. (English) Zbl 1028.65061 BIT 42, No. 3, 519-530 (2002). 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) Cited in 1 ReviewCited in 25 Documents 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 Keywords:Newton Method; nonlinear operator equation; nonlinear Hammerstein integral equation; convergence; Banach space PDFBibTeX XMLCite \textit{J. A. Ezquerro} and \textit{M. A. Hernández}, BIT 42, No. 3, 519--530 (2002; Zbl 1028.65061)