M, M.George, S.Godavarma, G.2026-02-032025Numerical Algorithms, 2025, 99, 2, pp. 683-71510171398https://doi.org/10.1007/s11075-024-01893-xhttps://idr.nitk.ac.in/handle/123456789/20235In this paper, unified convergence analyses for a class of iterative methods of order three, five, and six are studied to solve the nonlinear systems in Banach space settings. Our analysis gives the number of iterations needed to achieve the given accuracy and the radius of the convergence ball precisely using weaker conditions on the involved operator. Various numerical examples have been taken to illustrate the proposed method, and the theoretical convergence has been validated via these examples. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.DynamicsFréchet derivativeIterative methodsNonlinear system