A Unified Local Convergence for Jarratt-type Methods in Banach Space under Weak Conditions

Santhosh George, Ioannis K Argyros

Abstract

We present a unified local convergence analysis for Jarratt-type meth-
ods in order to approximate a solution of a nonlinear equation in a Ba-
nach space setting. Our methods include the Jarratt;Inverse free Jarratt;
super-Halley and other high order methods. The convergence ball and
error estimates are given for these methods under the same conditions.
Numerical examples are also provided in this study.