Chapter 1

Many classes of optimal Jarratt-type fourth-order methods

Abstract/Preface

In this paper, we have presented a family of two-point fourth order iterative methods without memory based on power mean using a weight function. The family of fourth order methods is optimal in the sense of Kung-Traub hypothesis. In terms of computational point of view, our methods require three evaluations (one function and two first derivatives) to get fourth order. Hence, these methods have high efficiency index 1.5874. Some known results can be regarded as particular cases of our family of methods. Some numerical examples are tested to know the performance of the methods which verifies the theoretical results.