The Secant method for nondifferentiable operators

In this paper, we use the Secant method to find a solution of a nonlinear operator equation in Banach spaces. A semilocal convergence result is obtained. For that, we consider a condition for divided differences which generalizes the usual ones, i.e., Lipschitz continuous or Hölder continuous conditions. Besides, we apply our results to approximate the solution of a nonlinear equation.