On The Convergence And Application Of Newton's Method Under Weak HÖlder Continuity Assumptions

The principle of majorizing sequences is used to show local and semilocal convergence of Newton's method to a locally unique solution of an operator equation in a Banach space setting, when the operator involved satisfies a Hölder and center Hölder continuity condition. Our convergence conditions are weaker; error bounds on the distances involved finer and the location of the solution more precise than in earlier results.

Keywords:

• Newton's Method
• Banach Space
• Majorizing Sequence
• Hölder Condition
• Lipschitz Condition
• Radius Of Convergence
• Semilocal/local Convergence