A convergence analysis and applications for the Newton-Kantorovich method in K-normed spaces

We study the local and semilocal convergence of the Newton-Kantorovich method to a solution of a nonlinear operator equation on aK-normed space setting. Using more precise majorizing sequences than before we show that in the semilocal case finer error bounds can be determined on the distances involved and an at least as precise information on the location of the solution as in earlier results. In the local case we show that a larger radius of convergence can be obtained.