Degree of convergence of modified averaged iterations for fixed points problems and operator equations

Let HH be a real Hilbert space. We propose a modification for averaged mappings to approximate the unique fixed point of a mapping T:H→HT:H→H such that TT is boundedly Lipschitzian and −T−T is monotone. We not only prove strong convergence theorems, but also determine the degree of convergence. Using this result, an iteration process is given for finding the unique solution of the equation Ax=fAx=f, where A:H→HA:H→H is strongly monotone and boundedly Lipschitzian.