Abstract:The goal of this study is to investigate the local convergence of a three-step Newton-Traub technique for solving nonlinear equations in Banach spaces with a convergence rate of five. The first order derivative of a nonlinear operator is assumed to satisfy the generalized Lipschitz condition, i.e. the κ-average condition. Furthermore, a few results on the convergence of the same method in Banach spaces are developed under the assumption that the derivative of the operators satisfies the radius or center Lipsch… Show more
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