Semilocal convergence for a family of Chebyshev-Halley like iterations under a mild differentiability condition
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 Hlder 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. As well, 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.
semilocal convergence nonlinear operator equation r-order of convergence hammerstein integral equation variant chebyshev-halley iteration family 47j05 65j15 65h10