Solving equations using Newton's method under weak conditions on Banach spaces with a convergence structure

Abstract

We provide new semilocal results for Newton's method on Banach spaces with a convergence structure. Using more precise majorizing sequence we show that, under weaker convergence conditions than before, we can obtain finer error bounds on the distances involved and a more precise information on the location of the solution.

Keywords

• Newton's method
• Banach spaces with a convergence structure
• semilocal convergence
• Fréchet-derivative
• majorant principle
• fixed point