Ball Convergence of an Efficient High Order Iterative Method for Solving Banach Valued Equations

The aim of this article is to extend the applicability of a multi-point iterative method for solving equations involving Banach space valued operators. The method uses evaluations of : two vector values, two linear operators, one inverse of a linear operator and one frozen inverse of a linear operator per iteration. The ball convergence was established in earlier works on the m-dimensional space and requiring very high order derivatives. We only use hypotheses on the first derivative. Hence, we extend the applicability of this method. Moreover, estimations are given on a radius of convergence and the error distances based on generalized Lipschitz conditions not given before. Numerical examples are used to complete this article.