Relaxing convergence conditions for Newton's method (Q1587437)

The author considers a Newton method to solve the equation \(F(x)\in 0\), where \(F\) is a nonlinear Fréchet differentiable operator from Banach space \(X\) to Banach space \(Y\). The classical Lipschitz condition for the first derivative is replaced a weakened condition. Then the convergence is proved and an error estimate is given. The presented theory is illustrated by a nonlinear equation of Hammerstein type.