BALL CONVERGENCE RESULTS FOR A METHOD WITH MEMORY OF EFFICIENCY INDEX 1.8392 USING ONLY FUNCTIONAL VALUES - Argyros, I. K.; George, S. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2018)
We present a local convergence analysis for an one-step iterative method with memory of efficiency index 1.8392 to solve nonlinear equations. If the function is twice differentiable, then it was shown that the R-order of convergence is 1.8392. In this paper we use hypotheses up to the first derivative. This way we extend the applicability of this method. Moreover, the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented to illustrate the theoretical results.