On the Secant method for solving nonsmooth equations

In this study we are concerned with the problem of approximating a locally unique solution of an operator equation in Banach space using the Secant method. The differentiability of the operator involved is not assumed. Using a flexible point-based approximation, we provide a local as well as a semilocal convergence analysis for the Secant method. Our results are justified by numerical examples that cannot be handled with earlier works.