LOCAL CONVERGENCE OF A MULTI-POINT JARRATT-TYPE METHOD IN BANACH SPACE UNDER WEAK CONDITIONS - Argyros, I. K.; George, S. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2016)
We present a local convergence analysis of a multi-point Jarratt-type method of high convergence order in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first Fréchet-derivative of the operator involved. In contrast to earlier studies using hypotheses up to the third Fréchet-derivative [26]. Numerical examples are also provided in this study.