TY - JOUR
T1 - Local Convergence for a Fifth Order Traub-Steffensen-Chebyshev-Like Composition Free of Derivatives in Banach Space
AU - Ioannis K. Argyros & Santhosh George
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 160
EP - 168
PY - 2018
DA - 2018/11
SN - 11
DO - http://doi.org/10.4208/nmtma.OA-2017-0017
UR - https://global-sci.org/intro/article_detail/nmtma/10648.html
KW - 
AB - <p style="text-align: justify;">We present the local convergence analysis of a fifth order Traub-Steffensen-Chebyshev-like composition for solving nonlinear equations in Banach spaces. In earlier
studies, hypotheses on the Fréchet derivative up to the fifth order of the operator under consideration are used to prove the convergence order of the method although only
divided differences of order one appear in the method. That restricts the applicability
of the method. In this paper, we extended the applicability of the fifth order Traub-Steffensen-Chebyshev-like composition without using hypotheses on the derivatives of
the operator involved. Our convergence conditions are weaker than the conditions used
in earlier studies. Numerical examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.</p>