BALL CONVERGENCE THEOREMS FOR KING’S FOURTH-ORDER ITERATIVE METHODS UNDER WEAK CONDITIONS

Abstract

We present a local convergence analysis for King’s fourth-order iterative methods in order to approximate a solution of a nonlinear equation. We use hypotheses up to the first derivative in contrast to earlier studies such as [1, 7]–[27] using hypotheses up to the third derivative (or even higher). This way the applicability of these methods is extended under weaker hypotheses. Moreover the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples where earlier results cannot be used to solve equations but our results can be used are also presented in this study.