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Semilocal convergence for Halley’s method under weak Lipschitz condition |
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| Authors: | Xiubin Xu Yonghui Ling |
| Affiliation: | Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China |
| Abstract: | The semilocal convergence properties of Halley’s method for nonlinear operator equations are studied under the hypothesis that the second derivative satisfies some weak Lipschitz condition. The method employed in the present paper is based on a family of recurrence relations which will be satisfied by the involved operator. An application to a nonlinear Hammerstein integral equation of the second kind is provided. |
| Keywords: | Halley&rsquo s method Weak Lipschitz condition Recurrence relations Semilocal convergence Affine invariant Hammerstein integral equation |
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