Shahid Beheshti University Computational Mathematics and Computer Modeling with Applications (CMCMA) 2783-4859 1 1 2022 06 01 On the semi-local convergence of the Homeier method in Banach space for solving equations 63 68 102247 10.52547/CMCMA.1.1.63 EN Samundra Regmi Learning Commons, University of North Texas at Dallas, Dallas, TX, USA Ioannis Konstantinos Argyros Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA Santhosh George Department of Mathematical and Computational Sciences,National Institute of Technology Karnataka, India-575 025 0000-0002-3530-5539 Christopher I. Argyros Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA Journal Article 2022 02 15 In this paper we consider the semi-local convergence analysis of the Homeier method for solving nonlinear equation in Banach space. As far as we know no semi-local convergence has been given for the Homeier under Lipschitz conditions. Our goal is to extend the applicability of the Homeier method in the semi-local convergence under these conditions. We use majorizing sequences and conditions only on the first derivative which appear on the method for proving our results. Numerical experiments are provided in this study. https://cmcma.sbu.ac.ir/article_102247_b10080e3e390564d77c6c8eff4d4ec02.pdf