New perturbed iterations for a generalized class of strongly nonlinear operator inclusion problems in Banach spaces.
Newton's methods for variational inclusions under conditioned Fréchet derivative
Estimates of the radius of convergence of Newton's methods for variational inclusions in Banach spaces are investigated under a weak Lipschitz condition on the first Fréchet derivative. We establish the linear convergence of Newton's and of a variant of Newton methods using the concepts of pseudo-Lipschitz set-valued map and ω-conditioned Fréchet derivative or the center-Lipschitz condition introduced by the first author.