BALL CONVERGENCE OF AN EIGHTH ORDER- ITERATIVE SCHEME WITH HIGH EFFICIENCY ORDER IN BANACH SPACE - Argyros, I. K.; George, S. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2019)
We present a local convergence analysis of an eighth order- iterative method in order to approximate a locally unique solution of an equation in Banach space setting. Earlier studies such as \cite{13, 18} have used hypotheses up to the fourth derivative although only the first derivative appears in the definition of these methods. In this study, we only use the hypothesis of the first derivative. This way we expand the applicability of these methods. Moreover, we provide a radius of convergence, a uniqueness ball and computable error bounds based on Lipschitz constants. Numerical examples computing the radii of the convergence balls as well as examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.