Ball convergence for a novel sixth order iterative method under hypothesis only on the first derivative

Abstract

 

 

We present a   local convergence analysis of a sixth  order iterative method  using only the first  derivative for solving equations in order to  approximate  a solution of a nonlinear equation. In earlier studies such as \cite{28}  hypotheses on the fifth  derivatives are used.   Thus by using only first derivative, we  extended the applicability of these methods.  Moreover the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples  are also presented in this study.