Convergence for a class of multi-point modified Chebyshev-Halley methods under the relaxed conditions
The authors consider semilocal convergence for a class of multi-point modified Chebyshev-Halley methods for solving equations \(F(x)=0\), where \(X,Y\) are Banach spaces and \(F: \Omega \subseteq X \rightarrow Y\) is a nonlinear operator on a non-empty open convex subset \(\Omega\). The methods are more general than the methods presented in their previous works (see [ibid. 64, No. 1, 105--126 (2013; Zbl 1279.65065)]). Moreover, the convergence conditions are also relaxed. They prove a convergence theorem to show the existence and uniqueness of the solution. The results of numerical experiments are also presented and discussed.
scientific article; zbMATH DE number 6418191