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

ABSTRACT

In this article, we deal with an iteration method for approximating a fixed point of a contraction mapping using 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 domain for the fixed point. Moreover, some numerical examples are considered.

KEYWORDS:

• Almost complete
• convergence
• confidence domain
• fixed point iteration
• Mann’s algorithm
• rate of convergence
• Stochastic methods

SUBJECT CLASSIFICATIONS:

• 76M35
• 60H35

Acknowledgments

The authors are thankful to reviewers for their careful reading and suggested comments.