Argyros, I.K.George, S.Argyros, M.2026-02-042022Communications on Applied Nonlinear Analysis, 2022, 29, 1, pp. 91-1021074133Xhttps://idr.nitk.ac.in/handle/123456789/22825The aim of this article is to extend the local as well as the semi-local convergence analysis of multi-point iterative methods using center Lipschitz conditions in combination with our idea, of the restricted convergence region. It turns out that this way a finer convergence analysis for these methods is obtained than in earlier works and without additional hypotheses. Numerical examples favoring our technique over earlier ones completes this article. © 2022, International Publications. All rights reserved.Banach spaceLocal-semi-local convergence analysisMulti-point iterative methods