Solving non-differentiable equations by a new one-point iterative method with memory

We construct a new iterative method for approximating the solutions of nonlinear operator equations, where the operator involved is not differentiable. The algorithm proposed does not need to evaluate derivatives and is more efficient than the secant method. For this, we extend a result of Traub for one-point iterative methods to one-point iterative methods with memory.

► We solve non-differentiable equations by a one-point iterative method with memory. ► Iterative method does not need to evaluate derivatives. ► Iterative method is more efficient than the secant method. ► We extend a result of Traub for one-point iterative methods to one-point iterative methods with memory.