Ball convergence theorems for unied three step Newton-like methods of high convergence order

  • Ioannis K. Argyros Cameron University
  • Santhosh George 2Department of Mathematical and Computational Sciences, NIT Karnataka, India-575 025,


We present a local convergence analysis for eighth-order variants of Newton's method in order to approximate a solution of a nonlinear equation. We use hypotheses up to the rst derivative in contrast to earlier studies such as [8]{[12], [24] using hypotheses up to the seventh derivative. This way the applicability of these methods is extended under weaker hypotheses. Moreover the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented in this study.

Author Biography

Ioannis K. Argyros, Cameron University
Professor Dr.Of Mathematics