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* This work was supported by National Science Foundation grant DMS 9404431.In this paper we prove that the Newton method applied to the
generalized equation y ∈ f(x) + F(x) with a C^1 function f and a set-valued map
F acting in Banach spaces, is locally convergent uniformly in the parameter y if
and only if the map (f +F)^(−1) is Aubin continuous at the reference point. We also
show that the Aubin continuity actually implies uniform Q-quadratic convergence
provided that the derivative of f is Lipschitz...
We prove that the generator of any uniformly bounded set-valued Nemytskij operator acting between generalized Hölder function metric spaces, with nonempty compact and convex values is an affine function with respect to the function variable.
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