  This work deals with the Mann's stochastic iteration algorithm under strong
mixing random errors. We establish the Fuk-Nagaev's inequalities that enable us
to prove the almost complete convergence with its corresponding rate of
convergence. Moreover, these inequalities give us the possibility of
constructing a confidence interval for the unique fixed point. Finally, to
check the feasibility and validity of our theoretical results, we consider some
numerical examples, namely a classical example from astronomy.

Probability