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Sociedad Colombiana de Matemáticas:Publicaciones

Revista Colombiana de Matemáticas

Volumen 34 [2] (2000)Páginas 49-56

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.

Palabras claves. Set-valued maps, Aubin continuity, generalized equa-tions, Newton's method, superlinear uniform convergence

Codigo AMS. 1991 Primary 47HO4. Secondary 65K10

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