Results on Newton methods. II: Perturbed Newton-like in generalized Banach spaces (Q1294209)

This paper is the second part of the results on Newton methods [for the first part see ibid. 102, 203-222 (1999; reviewed above)]. The author studies the problem of approximating a locally unique solution of a nonlinear operator equation in a generalized Banach space. He uses the idea of a generalized norm which is defined to be a map from a linear space into a partially ordered Banach space. Using perturbed Newton-like methods the author generates an iteration that converges to a solution, even in the case when iterates are not computed exactly. The convergence results and error estimates are improved when compared with the real norm theory. Applications to nonlinear integral and differential equations are suggested.