Solving a special case of conservative problems by Secant-like methods

We study a class of Secant-like iterations for solving nonlinear equations in Banach spaces. A semilocal convergence result is obtained, where the first order divided difference of the nonlinear operator is Hölder continuous. For that, we use a technique based on a new system of recurrence relations to obtain existence-uniqueness domains of the solution and a priori error bounds. These results are applied to solve a special case of conservative problems.