Local convergence of generalized Mann iteration

The local convergence of generalized Mann iteration is investigated in the setting of a real Hilbert space. As application, we obtain an algorithm for estimating the local radius of convergence for some known iterative methods. Numerical experiments are presented showing the performances of the proposed algorithm. For a particular case of the Ezquerro-Hernandez method (Ezquerro and Hernandez, J. Complex., 25:343-361: 2009), the proposed procedure gives radii which are very close to or even identical with the best possible ones.