Local convergence and basins of attraction of a two-step Newton-like method for equations with solutions of multiplicity greater than one

Abstract

Let S = ℝ or S = ℂ, D ⊆ S be convex and let F : D → S be a differentiable function. We shall approximate solutions x of the equation F(x) = 0, (5.1) Many problems from Applied Sciences including engineering can be solved finding the solutions of equations in a form like (5.1) [4,5, 20,25, 31,39, 43–45].