On the Accessibility of Newton’s Method under a Hölder Condition on the First Derivative

Abstract

We see how we can improve the accessibility of Newton’s method for approximating a solution of a nonlinear equation in Banach spaces when a center Hölder condition on the first derivative is used to prove its semi-local convergence.

Keywords

• Newton’s method
• semi-local convergence
• recurrence relations
• domain of parameters
• nonlinear system