Abstract
AbstractThe aim of this study is to extend the applicability of an eighth convergence order method from thek−dimensional Euclidean space to a Banach space setting. We use hypotheses only on the first derivative to show the local convergence of the method. Earlier studies use hypotheses up to the eighth derivative although only the first derivative and a divided difference of order one appear in the method. Moreover, we provide computable error bounds based on Lipschitz-type functions.
Highlights
The aim of this study is to extend the applicability of an eighth convergence order method from the k− dimensional Euclidean space to a Banach space setting
We use hypotheses only on the rst derivative to show the local convergence of the method
Earlier studies use hypotheses up to the eighth derivative only the rst derivative and a divided di erence of order one appear in the method
Summary
Abstract: The aim of this study is to extend the applicability of an eighth convergence order method from the k− dimensional Euclidean space to a Banach space setting. We use hypotheses only on the rst derivative to show the local convergence of the method. Improving the order of convergence of iterative method for solving (1.1) is an important problem in mathematics.
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