Convergence of derivative free iterative methods

We present the local as well as the semi-local convergence of some iterative methods free of derivatives for Banach space valued operators. These methods contain the secant and the Kurchatov method as special cases. The convergence is based on weak hypotheses specializing to Lipschitz continuous or Holder continuous hypotheses. The results are of theoretical and practical interest. In particular the method is compared favorably ¨ to other methods using concrete numerical examples to solve systems of equations containing a nondifferentiable term.