A convergence theorem for Newton-like methods under generalized Chen- Yamamoto-type assumptions
The author provides sufficient conditions for the convergence of a Newton-like method to a locally unique solution of a nonlinear operator equation with a nondifferentiable term in a Banach space setting. He assumes the existence of real-valued functions of two variables that are upper bounds on the governing operator. Using a majorant method, the author proves that the sequence generated by the Newton-like method is well-defined and converges to a solution of the above-mentioned equation. An error estimate is given.
scientific article; zbMATH DE number 554117