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.b180429
Published 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
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