Local convergence of deformed Halley method in Banach space under Holder continuity conditions

We present a local convergence analysis for deformed Halley method in order to approximate a solution of a nonlinear equation in a Banach space setting. Our methods include the Halley and other high order methods under hypotheses up to the first Frechet-derivative in contrast to earlier studies using hypotheses up to the second or third Frechet-derivative. The convergence ball and error estimates are given for these methods. Numerical examples are also provided in this study.