Improved local convergence analysis for a three point method of convergence order 1.839

Abstract

In this paper, we present a local convergence analysis of a three point method with convergence order 1.839 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. 2019 Korean Mathematical Society.