A generalization of the Newton—Kantorovich theorem in a banach space - Chuiko, S.M. (Reports of the National Academy of Sciences of Ukraine, 2018)
We present a modification of the Newton—Kantorovich method for nonlinear operator equations in a Banach space. We prove, under certain conditions, that this modified Newton—Kantorovich method has quadratic convergence. The modified Newton—Kantorovich method is used to solve some nonlinear integral and integral- differential equations.