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.