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 Improved local convergence analysis for a three point method of convergence order 1.839$\cdots$ Bull. Korean Math. Soc.Published online 2019 May 16 Ioannis K. Argyros, Yeol Je Cho, and Santhosh George Cameron University, Gyeongsang National University, 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$\cdots$ for approximating a locally unique solution of a nonlinear operator equation in setting of Banach spaces. Using weaker hypotheses than in earlier studies such as \cite{17}, 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 : 65J15, 65J22 Full-Text :