Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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IMPROVED LOCAL CONVERGENCE ANALYSIS FOR A THREE POINT METHOD OF CONVERGENCE ORDER 1.839…

  • Argyros, Ioannis K. (Department of Mathematical Sciences Cameron University) ;
  • Cho, Yeol Je (Department of Mathematics Education Gyeongsang National University) ;
  • George, Santhosh (Department of Mathematical and Computational Sciences National Institute of Technology Karnataka)
  • Received : 2018.05.02
  • Accepted : 2019.03.08
  • Published : 2019.05.31
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Abstract

In this paper, we present a local convergence analysis of a three point method with convergence order $1.839{\ldots}$ 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.

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