HIGHER ORDER DERIVATIVE-FREE ITERATIVE METHODS WITH AND WITHOUT MEMORY IN BANACH SPACE UNDER WEAK CONDITIONS

Abstract

We study the method considered in Ahmad et al. (2016), for solving systems of nonlinear equations, modified suitably to include the nonlinear equations in Banach spaces. We use the idea of restricted convergence domains instead of Taylors expansion in our convergence analysis and our conditions are weaker than the conditions used in earlier studies. Numerical examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.