| Article ID: | iaor20123943 |
| Volume: | 153 |
| Issue: | 3 |
| Start Page Number: | 779 |
| End Page Number: | 793 |
| Publication Date: | Jun 2012 |
| Journal: | Journal of Optimization Theory and Applications |
| Authors: | Wang Xiuhua, Kou Jisheng, Gu Chuanqing |
| Keywords: | programming: nonlinear |
In this paper, we consider the semilocal convergence of a class of modified super‐Halley methods for solving nonlinear equations in Banach spaces. The semilocal convergence of this class of methods is established by using recurrence relations. We construct a system of recurrence relations for the methods, and based on it, we prove an existence–uniqueness theorem that shows the