Does Newton's method for set-valued maps converges uniformly in mild differentiability context?
- Autores: Pietrus Alain
- Localización: Revista Colombiana de Matemáticas, ISSN-e 0034-7426, Vol. 34, Nº. 2, 2000, págs. 49-56
- Idioma: inglés
- Enlaces
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Resumen
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.
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