The College of Education for Pure Sciences at the University of Basrah  organized a scientific lecture entitled (New effective iterative methods based on the squared formula of Haar waves with various means for solving nonlinear equations).
The lecture presented by the researcher (Weam Mahdi Aktami) included the study, we proposed some new iterative methods for solving nonlinear equations based on two families of power modes and Gini modes, using the Wavelet-Hare quadratic formula. Some of those arguments used are the arithmetic mean, the geometric mean, the harmonic mean, the antiharmonic mean, the root mean square mean and the root mean square mean, with other special cases. We also transform the two-step iterative methods into one-step methods using the Taylor expansion, and then transform it from those one-step methods into two- and three-step methods using the estimator-corrector technique with approximation of the derivatives once and without again for the purpose of reducing the number of arithmetic functions, in Each step, into five, three and four functions with sixth, fourth and eighth order convergence, respectively. Thus, the indices of efficiency for the new proposed modalities are
6^(1/5)≃1.431, 4^(1/3)≃1.587, and 8^(1/4)≃1.682, respectively.
Finally, many numerical examples are given to illustrate the efficiency and performance of these new methods and to compare them with other related iterative methods.