Semilocal Convergence of a Class of Modified Super-Halley Methods in Banach Spaces

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 R-order of the methods.

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