Several iterative methods with memory using self-accelerators

We derive new iterative methods with memory for approximating a simple zero of a nonlinear single variable function. To this end, we first consider several modifications on some existing optimal classes without memory in such a way that their extensions to cases with memory could obtain the higher efficiency index 1214≈1.86120. Furthermore, we construct our main method with memory using three self-accelerators. It is demonstrated that this new scheme possesses the very high efficiency index 7.2381413≈1.93438.