Samundra Regmi - Learning Commons, University of North Texas at Dallas, Dallas, TX, USA
Ioannis Konstantinos Argyros - Department of Mathematical Sciences, Cameron University, Lawton, OK ۷۳۵۰۵, USA
Santhosh George - Department of Mathematical and Computational Sciences,National Institute of Technology Karnataka, India-۵۷۵ ۰۲۵
Christopher I. Argyros - Department of Computing and Technology, Cameron University, Lawton, OK ۷۳۵۰۵, USA

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.

semi-local convergence, Homeier method, iterative methods, Banach space, convergence criterion