A study on the local convergence of a Steffensen-King-type iterative method

Abstract

We study the local convergence of a  Steffensen-King-type method  to approximate a locally unique solution of a nonlinear equation. Earlier studies such as \cite{14,15,17} show convergence under hypotheses on the third derivative or even higher. The convergence in this study is shown under hypotheses on the first derivative. Hence, the applicability  of the method is expanded.  Finally, numerical examples are also provided in this study.