In this note we extend the validity of the mesh-independence principle for nonlinear operator equations and their discretizations to include operators whose derivatives are only Hölder continuous. In… (More)

We extend the applicability of the Gauss–Newton method for solving singular systems of equations under the notions of average Lipschitz–type conditions introduced recently in Li et al. (J Complex… (More)

We provide a semilocal convergence analysis for a certain class of secant-like methods considered also in Argyros (J Math Anal Appl 298:374–397, 2004, 2007), Potra (Libertas Mathematica 5:71–84,… (More)

On The Convergence And Application Of Newton's Method Under Weak HÖlder Continuity Assumptions Ioannis Argyros To cite this article: Ioannis Argyros (2003) On The Convergence And Application Of… (More)

We use inexact Newton iterates to approximate a solution of a nonlinear equation in a Banach space. Solving a nonlinear equation using Newton iterates at each stage is very expensive in general. That… (More)