Argyros, I.K.George, S.2026-02-052017International Journal of Applied and Computational Mathematics, 2017, 3, 4, pp. 3295-330423495103https://doi.org/10.1007/s40819-016-0297-xhttps://idr.nitk.ac.in/handle/123456789/25402In this paper we consider the Kantorovich’s theorem for solving generalized equations F(x) + Q(x) ? 0 using Newton’s method, where F is a Fréchet differentiable function and Q is a set-valued and maximal monotone function acting between Hilbert spaces. We used our new idea of restricted convergence domains to obtain better location about where the iterates are located leading to a tighter convergence analysis than in the earlier studies and under the same or less computational cost of the majorant functions involved. © 2016, Springer India Pvt. Ltd.Generalized equationKantorovich’s theoremMaximal monotone operatorNewton’s methodRestricted convergence domains