Argyros I.K.George S.Erappa S.M.2021-05-052021-05-052020Boletim da Sociedade Paranaense de Matematica Vol. 39 , 6 , p. 195 - 210https://doi.org/10.5269/BSPM.42132https://idr.nitk.ac.in/handle/123456789/15456The concept of regular smoothness has been shown to be an appropriate and powerfull tool for the convergence of iterative procedures converging to a locally unique solution of an operator equation in a Banach space setting. Motivated by earlier works, and optimization considerations, we present a tighter semi-local convergence analysis using our new idea of restricted convergence domains. Numerical examples complete this study. © 2020 Boletim da Sociedade Paranaense de Matematica. All rights reserved.Article