On the Kurchatov method for solving equations under weak conditions

We present a new convergence analysis for the Kurchatov method in order to solve nonlinear equations in a Banach space setting. In the semilocal convergence case, the sufficient convergence conditions are weaker than in earlier studies such as Argyros (2005, 2007), Ezquerro et al. (2013) and Kurchatov (1971). This way we extend the applicability of this method. Moreover, in the local convergence case, our radius of convergence is larger leading to a wider choice of initial guesses and fewer iterations to achieve a desired error tolerance. Numerical examples are also presented.