On the convergence of inexact two-step Newton-like algorithms using recurrent functions

Using our new concept of recurrent functions, we approximate a locally unique solution of a nonlinear equation by an inexact two-step Newton-like algorithm in a Banach space setting. Our semilocal analysis provides tighter error bounds than before, and in many interesting cases, weaker sufficient convergence conditions. Applications including the solution of a nonlinear Chandrasekhar-type integral equation appearing in radiative transfer, and a two point boundary value problem with a Green kernel are also provided in this study.