BALL CONVERGENCE OF A FIFTH ORDER METHOD FOR SOLVING EQUATIONS UNDER WEAK CONDITIONS

We present a local convergence analysis for a family of Steffensen-type fifth-order methods in order to approximate a solution of a nonlinear equation. We use hypotheses up to the second derivative in contrast to earlier studies such as using hypotheses up to the sixth derivative. 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 are also presented in this study.