Exponential inequalities for Mann's iterative scheme with functional random errors

Abstract

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.

arXiv admin note: text overlap with arXiv:1403.2546 by other authors