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

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Advances in the Theory of Nonlinear Analysis and its Application
Volume:2 Issue:1
Local convergence for a Chebyshev-type method in Banach space free of derivatives

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

Authors : Santhosh George, Ioannis K Argyros

Pages : 62-69

Doi:10.31197/atnaa.400459

View : 10 | Download : 6

Publication Date : 2018-03-25

Article Type : Research Paper

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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