Convergence conditions on the second derivative of the operator

Abstract

As we have pointed out in the preface to the textbook, our main goal is to obtain semilocal convergence results for Newton’s method under different conditions for the operator involved. In Chapter 1, we have seen that the application of the majorant principle of Kantorovich is not easy if condition (A2) is not satisfied. For this, we have introduced a more general definition of majorant function than that given by Kantorovich and, from Theorem 1.27, we have seen the conditions that must be satisfy the scalar function candidate to be a majorant function.