Argyros, I.K.George, S.Argyros, C.I.2026-02-042022Communications on Applied Nonlinear Analysis, 2022, 29, 1, pp. 81-901074133Xhttps://idr.nitk.ac.in/handle/123456789/22827We present a semi-local convergence analysis of m−step iterative methods in order to approximate a locally unique solution for Banach space valued equations. Our analysis extends the applicability of these methods. Using the center-Lipschitz con-dition, we determine a more precise domain containing the iterates leading to at least as tight Lipschitz constants as well as a finer semi-local convergence analysis than in earlier studies. Numerical examples are also presented, where the convergence criteria are tested and compared favorably to existing ones. © 2022, International Publications. All rights reserved.Banach spaceFréchet-derivativeM−step iterative methodSemi-local convergence