Does Newton's method for set-valued maps converges uniformly in mild differentiability context?

In this article, we study the existence of Newton-type sequence for solving the equation y ϵ f(?) + F(?) where y is a small parameter, f is a function whose Fréchet derivative satisfies a Holder condition of the form II∇f(?_k) -∇f(x₂)∥ ≤ K ∥lx₁ - x₂∥^d and F is a set-valued map between two Banach spaces X and Y. We prove that the Newton-type method y ∈ f(?_k) +∇f(?_k)(?_k+1 - ?_k ) +F(?_k+1), is locally convergent to a solution of  y ϵ f(?) + F(?) if the set valued map (f(x* )+ ∇f(x* )(∙-?*)+F(∙))^-1 is Aubin continuous at (0,?*) where ?* is a solution of 0 ϵ f(?) + F(?). Moreover, we show that this convergence is superlinear uniformly in the parameter y and quadratic when d = 1.