Does Newton's method for set-valued
maps converges uniformly in
mild differentiability context?
Pietrus, Alain Université de Poitiers, Futuroscope Chasseneuil, FRANCE
Abstract.
In this article, we study the existence of Newton-type sequence for solving the equation where y is a small parameter, f is a function whose Fréchet derivative satisfies a Hölder condition of the form and F is a set-valued map between two Banach spaces X and Y . We prove that the Newton-type method , is locally convergent to a solution of if the set valued map is Aubin continuous at (0; x*) where x* is a solution of . Moreover, we show that this convergence is superlinear uniformly in the parameter y and quadratic when d = 1.
