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Semilocal convergence for a family of Chebyshev-Halley like iterations under a mild differentiability condition. (English) Zbl 1294.47093
Summary: The semilocal convergence of a family of Chebyshev-Halley like iterations for nonlinear operator equations is studied under the hypothesis that the first derivative satisfies a mild differentiability condition. This condition includes the usual Lipschitz condition and the Hölder condition as special cases. The method employed in the present paper is based on a family of recurrence relations. The R-order of convergence of the methods is also analyzed. Moreover, an application to a nonlinear Hammerstein integral equation of the second kind is provided. Furthermore, two numerical examples are presented to demonstrate the applicability and efficiency of the convergence results.

MSC:
47J25 Iterative procedures involving nonlinear operators
65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
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