Argyros, I.K.George, S.2026-02-052017Nonlinear Functional Analysis and Applications, 2017, 22, 1, pp. 41-5812291595https://idr.nitk.ac.in/handle/123456789/25664We present a new convergence analysis for the Kurchatov method using our new idea of restricted convergence domains in order to solve nonlinear equations in a Banach space setting. The suffcient convergence conditions are weaker than in earlier studies. Hence, we extend the applicability of this method. Moreover, our radius of convergence is larger leading to a wider choice of initial guesses and fewer iterations to achieve a desired error tolerance. Numerical examples are also provided showing the advantages of our approach over earlier work. © 2017 Kyungnam University Press.Banach spaceDivided differenceKurchatov methodLocal-semilocal convergenceNewton's method