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Volume 1, Issue 1

Newton variants for solving equations in Banach space using restricted convergence regions

Pages: 40 – 50


Ioannis K. Argyros, Santhosh George


We study a three step Newton variant method for solving equations involving Banach space valued operators. The local as well as the semi-local convergence analysis uses weaker conditions than before for such methods in combination with our idea of the restricted convergence region. This way we locate a more precise region containing the iterates leading to tighter functions and parameters and to the extension of the applicability of the present method. The same technique can be used to extend the applicability of similar methods. Numerical examples validate our theoretical results.

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Received: 18 February 2019; Accepted: 21 August 2019.