Exponential inequalities for Mann's iterative scheme with functional   random errors
  In this work, we deal with an iteration method for approximating a fixed point of a contraction mapping using the Mann's algorithm under functional random errors. We first show its almost complete convergence to the fixed point by mean of an exponential inequality and then we specify the induced rate of convergence. We finally build a confidence set for the fixed point. 
Bahia Barache, Idir Arab, Abdelnasser Dahmani
math.PR math.FA