Argyros, I.K.George, S.2026-02-052021Applicationes Mathematicae, 2021, 48, 2, pp. 209-22012337234https://doi.org/10.4064/am2392-1-2020https://idr.nitk.ac.in/handle/123456789/23401We introduce highly efficient solvers of nonlinear equations involving Banach space valued operators. The local convergence is based only on the first Fréchet derivative in contrast to earlier works using derivatives up to order seven to show the sixth order of convergence. Hence, we extend the applicability of these methods. Numerical examples are used to test the conditions of the theoretical results. © Instytut Matematyczny PAN, 2021.Banach spaceFréchet derivativelocal convergenceorder of convergence