## On some iterative methods for solving nonlinear equations.(English)Zbl 0818.65050

The paper is devoted to the study of nonlinear equations of the form $$f(x) + g(x) = 0$$ in Banach spaces, with $$f$$ a differentiable operator and $$g$$ a nondifferentiable but continuous operator. The main idea is to replace the first derivative of $$g$$ in the classical Newton method – which cannot be applied here – by the first-order divided difference of $$g$$. The obtained method consisting of a combination of Newton and chord methods has the same order of convergence as the chord method. A numerical example is also given.

### MSC:

 65J15 Numerical solutions to equations with nonlinear operators 47J25 Iterative procedures involving nonlinear operators