Expanding the applicability of inexact Newton methods using restricted convergence domains

We provide a new semilocal convergence analysis for the inexact Newton method in order to approximate a solution of a nonlinear equation in a Banach space setting. Using a new idea of restricted convergence domains we present a convergence analysis with the following advantages over earlier studies: larger convergence domain, tighter error bounds on the distances involved and an at least as precise information on the location of the solution. This way we expand the applicability of the inexact Newton method. Special cases and numerical examples are also provided.