Ball convergence comparison between three iterative methods in Banach space under hypothese only on the first derivative
We present a convergence ball comparison between three iterative methods for approximating a locally unique solution of a nonlinear equation in a Banach space setting. The convergence ball and error estimates are given for these methods under hypotheses only on the first Frechet derivative in contrast to earlier studies such as Adomian (1994) 1, Babajee et?al. (2008) 13, Cordero and Torregrosa (2007) 17, Cordero et?al. 18, Darvishi and Barati (2007) 19, using hypotheses reaching up to the fourth Frechet derivative although only the first derivative appears in these methods. This way we expand the applicability of these methods. Numerical examples are also presented in this study.