Geodesic
Newton's method for generalized equations under weak conditions
Serdica Mathematical Journal, Tome 49 (2023) no. 4, pp. 269-282.

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A local convergence analysis is developed for Newton’s method in order to approximate a solution of a generalized equations in a Banach space setting. The convergence conditions are based on generalized continuity conditions on the Fr´echet derivative of the operator involved and the Aubin property. The specialized cases of our results extend earlier ones using similar information.
Keywords: Banach space, local convergence, Newton's method, generalized equation, 34A34, 65B99, 65P30, 65H05 
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     title = {Newton's method for generalized equations under weak conditions},
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Argyros, Ioannis; George, Santhosh. Newton's method for generalized equations under weak conditions. Serdica Mathematical Journal, Tome 49 (2023) no. 4, pp. 269-282. http://geodesic.mathdoc.fr/item/SMJ2_2023_49_4_a3/