Local convergence of a class of multi-point Super–Halley methods in Banach spaces under weak conditions

Abstract

We present a local convergence analysis of a class of multi-point Super–Halley methods in order to approximate a solution of nonlinear equations in a Banach space setting. The semilocal convergence analysis of this method was studied by Wang
et. al. [24]. This work provides computable convergence ball and computable error bounds under weaker conditions than in [24]. Numerical examples are also provided in this study.