Abstract
In this work, we develop two families of optimal fourth order iterative methods requiring three evaluations. During each step, methods need evaluation of two derivatives and one function. According to the Kung–Traub conjecture an optimal iterative method without memory based on 3 evaluations could achieve an optimal convergence order of 4. The proposed iterative methods are especially befitting for finding zeros of functions whose derivative is easy to evaluate. For example, polynomial functions and functions defined via integrals.
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