Majorizing sequences for Newton's method from initial value problems (Q765273)

Let \(x^*\) be a solution of the equation \(F(x)=0\), where \(F\) is a nonlinear operator defined on a non-empty open convex domain \(\Omega\) of a Banach space \(X\) with a values in a Banach space \(Y\). The main idea of this paper is to generalize the semilocal convergence conditions given by Kantorovich for Newton's method, so that the condition \(\|F''(x)\| \leq k, x \in \Omega\), is relaxed in order that Newton's method can be applied to solve more equations. The Kantorovich technique based on a majorizing sequence used in the paper. The bibliography contains 15 sources.