Argyros, I.K.George, S.Erappa, S.M.2026-02-052020Boletim da Sociedade Paranaense de Matematica, 2020, 39, 6, pp. 195-210378712https://doi.org/10.5269/BSPM.42132https://idr.nitk.ac.in/handle/123456789/23668The 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.Kantorovich hypothesisMajorizing operatorNewton’s methodRegular smoothnessSecant method