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A one-parameter 4-point sixteenth-order King-type family of iterative methods which satisfy the famous Kung-Traub conjecture is proposed. The convergence of the family is proved, and numerical experiments are carried out to find the best member of the family. In most experiments, the best member was found to be a sixteenth-order Ostrowski-type method.

On a 4-Point Sixteenth-Order King Family of Iterative Methods for Solving Nonlinear Equations