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Local convergence for a Chebyshev-type method in Banach space free of derivatives. (English) Zbl 1412.65010

Summary: 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.

MSC:

65D10 Numerical smoothing, curve fitting
49M15 Newton-type methods
74G20 Local existence of solutions (near a given solution) for equilibrium problems in solid mechanics (MSC2010)
41A25 Rate of convergence, degree of approximation
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