- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 Improved local convergence analysis for a three point method of convergence order 1.839$\dots$ Bull. Korean Math. Soc. 2019 Vol. 56, No. 3, 621-629 https://doi.org/10.4134/BKMS.b180429Published online May 31, 2019 Ioannis K. Argyros, Yeol Je Cho, Santhosh George Cameron University; University of Electronic Science and Technology of China; National Institute of Technology Karnataka Abstract : In this paper, we present a local convergence analysis of a three point method with convergence order 1.839$\dots$ for approximating a locally unique solution of a nonlinear operator equation in setting of Banach spaces. Using weaker hypotheses than in earlier studies, we obtain: larger radius of convergence and more precise error estimates on the distances involved. Finally, numerical examples are used to show the advantages of the main results over earlier results. Keywords : Banach space, three point method, divided difference of order one-two, radius of convergence, local convergence MSC numbers : 65D10, 65D99, 65G99, 47H17, 49M15 Full-Text :