Results on Newton methods. I: A unified approach for constructing perturbed Newton-like methods in Banach space and their applications (Q5906392)

This paper is the first part of the results on Newton methods [for the second part see ibid. 102, No. 2-3, 223-236 (1999; reviewed below)]. The author introduces some new very general ways of constructing fast iterative methods for the solution of nonlinear operator equations. Convergence theorems are obtained using Newton-Kantorovich-type hypotheses and the majorant method in a Banach space setting. The monotone converence is examined in a partially ordered topological space setting. Some applications to the solution of nonlinear integral equations appearing in radiative transfer and nonlinear integral equation of Uryson type are also given.