Local convergence for a Chebyshev-type method in Banach space free of derivatives

Year 2018, Volume: 2 Issue: 1, 62 - 69, 25.03.2018

Santhosh George , Ioannis K Argyros

https://doi.org/10.31197/atnaa.400459

Abstract

This  paper is devoted to the study of a Chebyshev-type method  free of derivatives  for solving nonlinear equations in Banach spaces. Using the idea of restricted convergence domain, we extended the applicability of the Chebyshev-type methods.   Our convergence conditions are weaker than the  conditions used in earlier studies. Therefore the applicability of the method is extended.   Numerical examples  where earlier results cannot apply to solve equations but our results can apply are also given in this study.

Keywords

Chebyshev-type method, restricted convergence domain, radius of convergence

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