Ball convergence comparison between two
sixth order Newton–Jarratt composition method

Abstract. We compare the convergence balls of two sixth order Newton–Jarratt composition methods used to approximate a locally unique solution of an equation in a Banach space setting. Our convergence conditions involve only the first Fréchet derivative in contrast to earlier studies such as [13, 28] using hypotheses up to the seventh Fréchet-derivative of the operator involved. This way we expand the applicability of these methods. We also provide computable radii of convergence and error bounds based only on Lipschitz constants. We also present examples where earlier results cannot apply but our results apply to solve equations.