Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2019; 56(3): 621-629

Online first article May 16, 2019      Printed May 31, 2019

https://doi.org/10.4134/BKMS.b180429

Copyright © The Korean Mathematical Society.

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

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