Argyros, Ioannis K.; George, Santhosh Local convergence for a Chebyshev-type method in Banach space free of derivatives. (English) Zbl 1412.65010 Adv. Theory Nonlinear Anal. Appl. 2, No. 1, 62-69 (2018). 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. Cited in 2 Documents 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 Keywords:Chebyshev-type method; restricted convergence domain; radius of convergence; local convergence PDFBibTeX XMLCite \textit{I. K. Argyros} and \textit{S. George}, Adv. Theory Nonlinear Anal. Appl. 2, No. 1, 62--69 (2018; Zbl 1412.65010) Full Text: DOI