Argyros, I.K.Cho, Y.J.George, S.2026-02-052019Bulletin of the Korean Mathematical Society, 2019, 56, 3, pp. 621-62910158634https://doi.org/10.4134/BKMS.b180429https://idr.nitk.ac.in/handle/123456789/24797In 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.Banach spaceDivided difference of order one-twoLocal convergenceRadius of convergenceThree point method