Ball convergence of an efficient multi-step scheme for solving equations and systems of equations

Attention has been given recently to the study of local convergence of multi-step schemes to increase the convergence order for solving Banach space valued equations. The convergence criteria involve higher order derivatives, limiting applicability of these methods. In this study we use the first derivative only in our analysis to extend the usage of these schemes. The technique we use can be applied to other schemes to obtain the same advantages. Numerical experiments compare favorably our results to earlier ones.