A Family of Higher Order Scheme for Multiple Roots

We have developed a two-point iterative scheme for multiple roots that achieves fifth order convergence by using two function evaluations and derivative each iteration. Weight approach is utilized to frame the scheme. The weight named as R(?t) used, which of ?t, ?t ?t, i.e., ?t=?t1+a?t, where real number ?t=g(yt)g(xt)1m˜ multi-valued function. consistency newly generated methods ensured numerically through basins attraction. Four complex functions are considered compare new with existing schemes via attraction, all provided attraction possess reflection symmetry. Further, five numerical examples used verify theoretical results contrast presented some recognized order. obtained proved better than same nature.