Results on Newton methods. II: Perturbed Newton-like methods in generalized Banach spaces (Q1914614)

[For part I see ibid. 74, No. 2-3, 119-141 (1996; reviewed above).] The author continues to concern himself with approximating a locally unique solution of a nonlinear operator equation in a generalized Banach space. He provides convergence results and error estimates for perturbed Newton-like methods, which generate an iteration that converges to a solution of the equation. 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. The author thinks that in this way the metric properties of the examined problem can be analyzed more precisely. The convergence results obtained by him are improved compared with the real norm theory. Applications to nonlinear integral and differential equations are suggested.